sat questions

A politician claims that he is supported by a clear majority of voters. In a recent survey, 35 out of 51 randomly selected voters indicated that they would vote for the politician. Use a 5% significance level for the test. Use Table 1 .

a.

Select the null and the alternative hypotheses.

b.

Calculate the sample proportion. (Round your answer to 3 decimal places.)

Sample proportion

c.

Calculate the value of test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

d.

Calculate the p-value of the test statistic. (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and final answer to 4 decimal places.)

p-value

e.

What is the conclusion?

Consider the following contingency table.

B

Bc

A

22

24

Ac

28

26

a.

Convert the contingency table into a joint probability table. (Round your intermediate calculations and final answers to 4 decimal places.)

B

Bc

Total

A

Ac

Total

b.

What is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

c.

What is the probability that A and B occur? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

d.

Given that B has occurred, what is the probability that A occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

e.

Given that Ac has occurred, what is the probability that B occurs? (Round your intermediate calculations and final answer to 4 decimal places.)

Probability

f.

Are A and B mutually exclusive events?

g.

Are A and B independent events?

A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 72, 55, 49, 35, 39, 23, and 77. It can be assumed that weekday customer visits follow a normal distribution. Use Table 2 .

a.

Construct a 90% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.)

Confidence interval

to

b.

Construct a 99% confidence interval for the average number of customers who visit the salon on weekdays. (Round intermediate calculations to 4 decimal places, "sample mean" and "sample standard deviation" to 2 decimal places and "t" value to 3 decimal places, and final answers to 2 decimal places.)

Confidence interval

to

c.

What happens to the width of the interval as the confidence level increases?

Consider the following sample data:

x

22

36

10

31

11

37

28

32

y

28

44

36

36

34

37

39

33

b.

Calculate b1 and b0. What is the sample regression equation? (Round intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

y-hat = + x

c.

Find the predicted value for y if x equals 12, 17, and 22. (Round intermediate coefficient values and final answers to 2 decimal places.)

y-hat

If x = 12

If x = 17

If x = 22

India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too high to be sustainable. A demographer assumes the following probability distribution of the household size in India.

Household Size

Probability

1

0.04

2

0.13

3

0.15

4

0.22

5

0.17

6

0.15

7

0.11

8

0.03

a.

What is the probability that there are less than 5 members in a typical household in India? (Round your answer to 2 decimal places.)

Probability

b.

What is the probability that there are 5 or more members in a typical household in India? (Round your answer to 2 decimal places.)

Probability

c.

What is the probability that the number of members in a typical household in India is greater than 4 and less than 7 members? (Round your answer to 2 decimal places.)

Probability

Consider the following population data:

22

28

10

12

8

a.

Calculate the range.

Range

b.

Calculate MAD. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

MAD

c.

Calculate the population variance. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Population variance

d.

Calculate the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Population standard deviation

On a particularly busy section of the Garden State Parkway in New Jersey, police use radar guns to detect speeders. Assume the time that elapses between successive speeders is exponentially distributed with a mean of 19 minutes.

a.

Calculate the rate parameter λ. (Round your answer to 4 decimal places.)

Rate parameter λ

b.

What is the probability of a waiting time less than 13 minutes between successive speeders? (Round your answer to 4 decimal places.)

Probability

c.

What is the probability of a waiting time in excess of 27 minutes between successive speeders? (Round your answer to 4 decimal places.)

Probability

The following ANOVA table was obtained when estimating a multiple regression.

ANOVA

df

SS

MS

F

Significance F

Regression

2

188,492.30

94,246.15

60.08

4.86E-11

Residual

29

45,490.50

1,568.64

Total

31

233,982.80

a.

Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)

se

b-1.

Calculate the coefficient of determination. (Round your answer to 4 decimal places.)

Coefficient of determination

b-2.

Interpret the coefficient of determination.

c.

Calculate adjusted R2. (Round your answer to 4 decimal places.)

Adjusted R2

In order to estimate the mean 30-year fixed mortgage rate for a home loan in the United States, a random sample of 17 recent loans is taken. The average calculated from this sample is 4.85%. It can be assumed that 30-year fixed mortgage rates are normally distributed with a standard deviation of 0.5%. Compute 90% and 95% confidence intervals for the population mean 30-year fixed mortgage rate. Use Table 1 . (Round intermediate calculations to 4 decimal places, "z" value and final answers to 2 decimal places. Enter your answers as percentages, not decimals.)

Confidence Level

Confidence Interval

90%

%

to

%

95%

%

to

Consider the following hypotheses:

H0: p ≥ 0.37

HA: p < 0.37

Which of the following sample information enables us to reject the null hypothesis at α = 0.05 and at α = 0.10? Use Table 1 .

α = 0.05

α = 0.10

a.

x = 33; n = 100

b.

x = 80; n = 285

c.

= 0.34; n = 58

d.

= 0.34; n = 416

In a multiple regression with two explanatory variables and 117 observations, it is found that SSR = 4.51 and SST = 8.86.

a.

Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)

se

b.

Calculate the coefficient of determination R2. (Round your answer to 4 decimal places.)

R2

c.

Calculate adjusted R2. (Round your answer to 4 decimal places.)

Adjusted R2

A retailer is looking to evaluate its customer service. Management has determined that if the retailer wants to stay competitive, then it will have to have at least a 91% satisfaction rate among its customers. Management will take corrective actions if the satisfaction rate falls below 91%. A survey of 1,450 customers showed that 1,305 were satisfied with their customer service. Use Table 1 .

a.

Select the hypotheses to test if the retailer needs to improve its services.

b.

What is the value of the appropriate test statistic? (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

c.

Compute the p-value. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

p-value

d.

What is the conclusion?

Consider the following hypotheses:

H0: μ = 360

HA: μ ≠ 360

The population is normally distributed with a population standard deviation of 73. Use Table 1 .

a.

Use a 10% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

Critical value(s)

±

b-1.

Calculate the value of the test statistic with = 389 and n = 80. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

b-2.

What is the conclusion at α = 0.10?

c.

Use a 5% level of significance to determine the critical value(s) of the test. (Round your answer to 2 decimal places.)

Critical value(s)

±

d-1.

Calculate the value of the test statistic with = 335 and n = 80. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

d-2.

What is the conclusion at α = 0.05?

Use computer) Assume that X is a hypergeometric random variable with N = 55, S = 18, and n = 14. Calculate the following probabilities. (Round your answers to 4 decimal places.)

a. P(X = 8)

b. P(X ≥ 2)

c. P(X ≤ 4)

For a sample of 41 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). The regression results are shown.

ANOVA

df

SS

MS

F

Significance F

Regression

2

3,519,512

1,759,756.0

10.29454

5.9E-04

Residual

24

4,102,577

170,940.7

Total

26

7,622,089

a.

Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)

b-1.

What proportion of the variability in crime rate is explained by the variability in the explanatory variables? (Round your answer to 4 decimal places.)

Explained proportion

b-2.

What proportion is unexplained? (Round your answer to 4 decimal places.)

Unexplained proportion

Consider the following simple linear regression results based on 20 observations. Use Table 2 .

Coefficients

Standard Error

t Stat

p-value

Lower 95%

Upper 95%

Intercept

33.8605

4.4081

7.6814

0.0000

24.60

43.12

x1

0.3634

0.1204

3.0183

0.0074

0.11

0.62

a-1.

Choose the hypotheses to determine if the intercept differs from zero.

a-2.

At the 5% significance level, what is the conclusion to the hypothesis test? Does the intercept differ from zero?

b-1.

Construct the 95% confidence interval for the slope coefficient. (Negative values should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places,"tα/2,df" value to 3 decimal places and final answers to 2 decimal places.)

Confidence interval

to

b-2.

At the 5% significance level, does the slope differ from zero?

Consider the following hypotheses:

H0: μ = 33

HA: μ ≠ 33

The population is normally distributed. A sample produces the following observations:

38

31

34

36

33

38

28

Use the p-value approach to conduct the test at a 5% level of significance. Use Table 2 .

Click here for the Excel Data File

a.

Find the mean and the standard deviation. (Round intermediate calculations to 4 decimal places. Round your answers to 2 decimal places.)

Mean

Standard deviation

b.

Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

c.

Approximate the p-value of the test statistic.

d.

What is the conclusion?

Let P(A) = 0.59, P(B) = 0.24, and P(A ∩ B) = 0.14.

a.

Calculate P(A | B). (Round your answer to 2 decimal places.)

P(A | B)

b.

Calculate P(A U B). (Round your answer to 2 decimal places.)

P(A U B)

c.

Calculate P((A U B)c). (Round your answer to 2 decimal places.)

P((A U B)c)

The time required to assemble an electronic component is normally distributed with a mean and a standard deviation of 34 minutes and 20 minutes, respectively. Use Table 1 .

a.

Find the probability that a randomly picked assembly takes between 26 and 40 minutes. (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Probability

b.

It is unusual for the assembly time to be above 56 minutes or below 13 minutes. What proportion of assembly times fall in these unusual categories? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Proportion of assembly times

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 55% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 25%. There is only a 65% chance that she will find a tutor at such short notice.

a.

What is the probability that Christine fails the course? (Round your answer to 4 decimal places.)

Probability

b.

Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.)

Probability

Consider the following returns for two investments, A and B, over the past four years:

Investment 1:

5%

13%

–2%

7%

Investment 2:

3%

10%

–8%

13%

a-1.

Calculate the mean for each investment. (Round your answers to 2 decimal places.)

Mean

Investment 1

percent

Investment 2

percent

a-2.

Which investment provides the higher return?

b-1.

Calculate the standard deviation for each investment. (Round your answers to 2 decimal places.)

Standard Deviation

Investment 1

Investment 2

b-2.

Which investment provides less risk?

c-1.

Given a risk-free rate of 1.2%, calculate the Sharpe ratio for each investment. (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Sharpe Ratio

Investment 1

Investment 2

c-2.

Which investment has performed better?

Market observers are quite uncertain whether the stock market has bottomed out from the economic meltdown that began in 2008. In an interview on March 8, 2009, CNBC interviewed two prominent economists who offered differing views on whether the U.S. economy was getting stronger or weaker. An investor not wanting to miss out on possible investment opportunities considers investing $20,000 in the stock market. He believes that the probability is 0.30 that the market will improve, 0.37 that it will stay the same, and 0.33 that it will deteriorate. Further, if the economy improves, he expects his investment to grow to $28,000, but it can also go down to $17,000 if the economy deteriorates. If the economy stays the same, his investment will stay at $20,000.

a.

What is the expected value of his investment?

Expected value

$

b.

What should the investor do if he is risk neutral?

Investor invest the $20,000.

c.

Is the decision clear-cut if he is risk averse?

A car manufacturer is concerned about poor customer satisfaction at one of its dealerships. The management decides to evaluate the satisfaction surveys of its next 66 customers. The dealer will be fined if the number of customers who report favorably is between 26 and 33. The dealership will be dissolved if fewer than 26 report favorably. It is known that 62% of the dealer’s customers report favorably on satisfaction surveys. Use Table 1 .

a.

What is the probability that the dealer will be fined? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability

b.

What is the probability that the dealership will be dissolved? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability

The historical returns on a balanced portfolio have had an average return of 10% and a standard deviation of 14%. Assume that returns on this portfolio follow a normal distribution. Use the empirical rule for normal distributions to answer the following questions.

a.

What percentage of returns were greater than 38%? (Round your answer to 1 decimal place.)

Percentage of returns

%

b.

What percentage of returns were below −18%? (Round your answer to 1 decimal place.)

Percentage of returns

%

A machine that is programmed to package 5.35 pounds of cereal is being tested for its accuracy. In a sample of 16 cereal boxes, the sample mean filling weight is calculated as 5.35 pounds. It can be assumed that filling weights are normally distributed with a population standard deviation of 0.04 pound. Use Table 1 .

a-1.

Identify the relevant parameter of interest for these quantitative data.

a-2.

Compute the point estimate as well as the margin of error with 95% confidence. (Round intermediate calculations to 4 decimal places. Round "z" value and final answers to 2 decimal places.)

Point estimate

Margin of error

b-1.

Calculate the 95% confidence interval. (Use rounded margin of error. Round your answers to 2 decimal places.)

Confidence interval

to

b-2.

Can we conclude that the packaging machine is operating improperly?

c.

How large a sample must we take if we want the margin of error to be at most 0.01 pound with 95% confidence? (Round intermediate calculations to 4 decimal places. Round "z" value to 2 decimal places and round up your final answer to the next whole number.)

Sample size

Consider the following hypotheses:

H0: μ ≥ 100

HA: μ < 100

The population is normally distributed. A sample produces the following observations:

88

77

100

83

102

96

Use the critical value approach to conduct the test at a 5% level of significance. Use Table 2 .

a.

Find the mean and the standard deviation. (Round intermediate calculations to 4 decimal places. Round your answers to 2 decimal places.)

Mean

Standard deviation

b.

Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

c.

Calculate the critical value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 3 decimal places.)

Critical value

d.

What is the conclusion?

In a simple linear regression, the following information is given:

= − 23; = 42;

a.

Calculate b1. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)

b1

b.

Calculate b0. (Round intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

b0

c-1.

What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.)

y-hat = + x

c-2.

Predict y if x equals −22.(Round intermediate coefficient values and final answer to 2 decimal places.)

y-hat

Using data from 50 workers, a researcher estimates Wage = β0 + β1 Education + β2 Experience +β3 Age + ε, where Wage is the hourly wage rate and Education, Experience, and Age are the years of higher education, the years of experience, and the age of the worker, respectively. A portion of the regression results is shown in the following table.

Coefficients

Standard Error

t Stat

p-value

Intercept

7.27

3.99

1.43

0.0629

Education

1.03

0.37

3.54

0.0001

Experience

0.43

0.11

3.23

0.0020

Age

−0.01

0.06

−0.10

0.7920

a-1.

What is the point estimate for β1?

a-2.

Interpret this value.

a-3.

What is the point estimate for β2?

a-4.

Interpret this value.

b.

What is the sample regression equation? (Negative value should be indicated by a minus sign. Round your answers to 2 decimal places.)

y-hat = + Education + Experience + Age

c.

What is the predicted value for Age = 38, Education = 3 and Experience = 5. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

y-hat

Suppose that the average IQ score is normally distributed with a mean of 115 and a standard deviation of 11. In addition to providing the answer, state the relevant Excel commands. (Use Excel)

a.

What is the probability a randomly selected person will have an IQ score of less than 89? (Round your answer to 4 decimal places.)

Probability

b.

What is the probability that a randomly selected person will have an IQ score greater than 125? (Round your answer to 4 decimal places.)

Probability

c.

What minimum IQ score does a person have to achieve to be in the top 2.6% of IQ scores? (Round your answer to 2 decimal places.)

Minimum IQ score

Consider the following frequency distribution.

Class

Frequency

2 up to 4

15

4 up to 6

65

6 up to 8

75

8 up to 10

15

a.

Calculate the population mean. (Round your answer to 2 decimal places.)

Population mean

b.

Calculate the population variance and the population standard deviation. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Population variance

Population standard deviation

Acceptance sampling is an important quality control technique, where a batch of data is tested to determine if the proportion of units having a particular attribute exceeds a given percentage. Suppose that 15% of produced items are known to be nonconforming. Every week a batch of items is evaluated and the production machines are adjusted if the proportion of nonconforming items exceeds 19%. Use Table 1 .

a.

What is the probability that the production machines will be adjusted if the batch consists of 68 items? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability

b.

What is the probability that the production machines will be adjusted if the batch consists of 136 items? (Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

Probability

Assume that X is a binomial random variable with n = 27 and p = 0.92. Calculate the following probabilities. (Round your intermediate and final answers to 4 decimal places.)

a. P(X = 26)

b. P(X = 25)

c. P(X ≥ 25)

A social scientist would like to analyze the relationship between educational attainment and salary. He collects the following sample data, where Education refers to years of higher education and Salary is the individual’s annual salary in thousands of dollars:

Education

3

4

6

2

5

4

8

0

Salary

$39

48

62

47

75

53

107

50

a.

Find the sample regression equation for the model: Salary = β0 + β1Education + ε. (Round intermediate calculations to 4 decimal places. Enter your answers in thousands rounded to 2 decimal places.)

+ Education

b.

Interpret the coefficient for education.

c.

What is the predicted salary for an individual who completed 7 years of higher education? (Round intermediate coefficient values to 2 decimal places and final answer, in dollars, to the nearest whole number.)

$

A sample of patients arriving at Overbrook Hospital’s emergency room recorded the following body temperature readings over the weekend:

99.0

100.4

99.7

100.4

99.1

101.7

100.9

100.5

99.3

101.9

100.4

101.9

100.5

99.4

102.7

99.4

100.9

100.1

100.7

100.2

Click here for the Excel Data File

a.

Construct a stem-and-leaf diagram.

Stem

Leaf

b.

Interpret the stem-and-leaf diagram.

A manager of a local retail store analyzes the relationship between advertising and sales by reviewing the store’s data for the previous six months.

Advertising (in $100s)

Sales (in $1,000s)

198

122

55

43

54

42

53

41

200

124

160

130

Click here for the Excel Data File

a.

Calculate the mean of advertising and the mean of sales. (Round your answers to 2 decimal places.)

Mean

Advertising

Sales

b.

Calculate the standard deviation of advertising and the standard deviation of sales. (Round your answers to 2 decimal places.)

Standard Deviation

Advertising

Sales

c-1.

Calculate the covariance between advertising and sales. (Round your answer to 2 decimal places.)

Covariance

c-2.

Interpret the covariance between advertising and sales.

d-1.

Calculate the correlation coefficient between advertising and sales. (Round your answer to 2 decimal places.)

Correlation coefficient

d-2.

Interpret the correlation coefficient between advertising and sales.

The monthly closing stock prices (rounded to the nearest dollar) for Panera Bread Co. for the first six months of 2010 are reported in the following table. Use Table 2 .

Months

Closing Stock Price

January 2010

$200

February 2010

205

March 2010

208

April 2010

207

May 2010

209

June 2010

204

a.

Calculate the sample mean and the sample standard deviation. (Round intermediate calculations to 4 decimal places and "sample mean" and "sample standard deviation" to 2 decimal places.)

Sample mean

Sample standard deviation

b.

Compute the 90% confidence interval for the mean stock price of Panera Bread Co., assuming that the stock price is normally distributed. (Round "t" value to 3 decimal places, and final answers to 2 decimal places.)

Confidence interval

to

c.

What happens to the margin of error if a higher confidence level is used for the interval estimate?

Complete the following probability table. (Round Prior Probability answers to 2 decimal places and intermediate calculations and other answers to 4 decimal places.)

Prior Probability

Conditional Probability

Joint Probability

Posterior Probability

P(B)

0.49

P(A | B)

0.10

P(A ∩ B )

P(B | A)

P(Bc)

P(A | Bc)

0.34

P(A ∩ Bc)

P(Bc | A)

Total

P(A)

Total

A local restaurant is committed to providing its patrons with the best dining experience possible. On a recent survey, the restaurant asked patrons to rate the quality of their entrées. The responses ranged from 1 to 5, where 1 indicated a disappointing entrée and 5 indicated an exceptional entrée.

The results of the survey are as follows:

5

2

5

3

5

5

1

2

4

5

4

5

4

1

5

4

5

5

5

5

4

2

3

5

4

2

5

2

2

5

5

2

5

5

3

3

Click here for the Excel Data File

a.

Construct frequency and relative frequency distributions that summarize the survey’s results. (Do not round intermediate calculations. Round "relative frequency" to 3 decimal places.)

Rating

Frequency

Relative Frequency

5

4

3

2

1

Total

b.

Are patrons generally satisfied with the quality of their entrées?

At a new exhibit in the Museum of Science, people are asked to choose between 71 or 200 random draws from a machine. The machine is known to have 88 green balls and 82 red balls. After each draw, the color of the ball is noted and the ball is put back for the next draw. You win a prize if more than 58% of the draws result in a green ball. Use Table 1 .

a.

Calculate the probability of getting more than 58% green balls.(Round intermediate calculations to 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

n

Probability

71

200

b.

Would you choose 71 or 200 draws for the game?

A construction company in Naples, Florida, is struggling to sell condominiums. In order to attract buyers, the company has made numerous price reductions and better financing offers. Although condominiums were once listed for $350,000, the company believes that it will be able to get an average sale price of $255,000. Let the price of these condominiums in the next quarter be normally distributed with a standard deviation of $17,000. Use Table 1 .

a.

What is the probability that the condominium will sell at a price (i) Below $231,000?, (ii) Above $293,000? (Round "z" value to 2 decimal places and final answer to 4 decimal places.)

Probability

Below $231,000

Above $293,000

b.

The company is also trying to sell an artist’s condo. Potential buyers will find the unusual features of this condo either pleasing or objectionable. The manager expects the average sale price of this condo to be the same as others at $255,000, but with a higher standard deviation of $21,000. What is the probability that this condo will sell at a price (i) Below $231,000?, (ii) Above $293,000? (Round your answers to 4 decimal places.)

Probability

Below $231,000

Above $293,000

A random variable X is exponentially distributed with a mean of 0.17.

a-1.

What is the rate parameter λ? (Round your answer to 3 decimal places.)

Rate parameter λ

a-2.

What is the standard deviation of X? (Round your answer to 3 decimal places.)

Standard deviation X

b.

Compute P(X > 0.30). (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)

P(X > 0.30)

c.

Compute P(0.10 ≤ X ≤ 0.30). (Round intermediate calculations to 4 decimal places and final answer to 4 decimal places.)

P(0.10 ≤ X ≤ 0.30)

Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading.

Grade

Numerical Score

Probability

A

4

0.140

B

3

0.200

C

2

0.430

D

1

0.125

F

0

0.105

b.

Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)

Grade

P(X ≤ x)

F

D

C

B

A

c.

What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Probability

d.

What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)

Probability

The scheduled arrival time for a daily flight from Boston to New York is 9:30 am. Historical data show that the arrival time follows the continuous uniform distribution with an early arrival time of 9:16 am and a late arrival time of 9:56 am.

a.

After converting the time data to a minute scale, calculate the mean and the standard deviation for the distribution. (Round your answers to 2 decimal places.)

Mean

minutes

Standard deviation

minutes

b.

What is the probability that a flight arrives late (later than 9:30 am)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Probability

Consider the following hypotheses:

H0: μ ≥ 201

HA: μ < 201

A sample of 80 observations results in a sample mean of 198. The population standard deviation is known to be 20. Use Table 1 .

a.

What is the critical value for the test with α = 0.05 and with α = 0.01? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)

Critical Value

α = 0.05

α = 0.01

b-1.

Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Test statistic

b-2.

Does the above sample evidence enable us to reject the null hypothesis at α = 0.05?

c.

Does the above sample evidence enable us to reject the null hypothesis at α = 0.01?