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new_microsoft_word_document.docx1.A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a one-hour flight is 0.080.
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(a) |
What is the probability that both will fail? (Round your answer to 4 decimal places.) |
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Probability |
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(b) |
What is the probability that neither will fail? (Round your answer to 4 decimal places.) |
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Probability |
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(c) |
What is the probability that at least one fails? (Round your answer to 4 decimal places.) |
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Probability |
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2.
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A biometric security device using fingerprints erroneously refuses to admit 2 in 1,000 authorized persons from a facility containing classified information. The device will erroneously admit 2 in 1,001,000 unauthorized persons. Assume that 90 percent of those who seek access are authorized. |
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If the alarm goes off and a person is refused admission, what is the probability that the person was really authorized? (Round your answer to 5 decimal places.) |
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Probability |
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3.
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Given P(A) = 0.53, P(B) = 0.15. |
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If A and B are independent, find P(A ∩ B). (Round your answer to 4 decimal places.) |
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P(A ∩ B) |
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4. Which statement concerning the binomial distribution is correct?
Its PDF covers all integer values of X from 0 to n.
Its PDF is the same as its CDF when π = .50.
Its CDF shows the probability of each value of X.
Its CDF is skewed right when π < .50.
5If we desire α = .10, then a p-value of .13 would lead us to reject the null hypothesis.
True
False
6
Which distribution is most nearly appropriate to describe the number of fatalities in Texas in a given year due to poisonous snakebites?
Geometric
Hypergeometric
Binomial
Poisson
7
The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution?
1.9
1.1
1.7
1.3
8
The level of significance is not:
the chance of accepting a true null hypothesis.
the probability of a "false rejection."
the likelihood of rejecting the null hypothesis when it is true.
a value between 0 and 1.
9
If events A and B are mutually exclusive, the joint probability of the events is zero.
True
False
10
Which of the following is not a characteristic of the t distribution?
It is a continuous distribution.
It a symmetric distribution.
It has a mean of zero.
It is similar to the z distribution when n is small.
11
Events A and B are mutually exclusive if P(A ∩ B) = 0.
True
False
12
Regarding probability, which of the following is correct?
The union of events A and B consists of all outcomes in the sample space that are contained in both event A and event B.
When events A and B are mutually exclusive, then P(A ∩ B) = P(A) + P(B).
When two events A and B are independent, the joint probability of the events can be found by multiplying the probabilities of the individual events.
The probability of the union of two events can exceed one.
13
Which of the following is not a requirement of a binomial distribution?
Fixed number of trials
Constant probability of success
Equally likely outcomes
Only two possible Bernoulli outcomes
14
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Car security alarms go off at a mean rate of 2.4 per hour in a large Costco parking lot. |
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Find the probability that in an hour there will be (Round your answers to 4 decimal places.) |
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Probability |
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(a) |
no alarms |
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(b) |
fewer than five alarms |
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(c) |
more than eight alarms |
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15
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On average, 6 percent of all persons who are given a breathalyzer test by the state police pass the test (blood alcohol under 0.08 percent). Suppose that 200 breathalyzer tests are given. |
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(a) |
What is the expected number who pass the test? (Round your answer to the nearest whole number.) |
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Expected number |
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(b) |
What is the approximate Poisson probability that 5 or fewer will pass the test? (Round your answer to 4 decimal places.) |
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Poisson probability |
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[The following information applies to the questions displayed below.]
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Historically, 11 percent of a mail-order firm's repeat charge-account customers have an incorrect current address in the firm's computer database. |
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The number of customers out of 18 who have an incorrect address in the database is a binomial random variable with n = 18 and π = 0.11. |
rev: 05_22_2012
16.
Required information
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(a) |
What is the probability that none of the next 18 repeat customers who call will have an incorrect address? (Round your answer to 4 decimal places.) |
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Probability |
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17.
Required information
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(b) |
What is the probability that seven customer who call will have an incorrect address? (Round your answer to 4 decimal places.) |
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Probability |
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18.
Required information
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(c) |
What is the probability that eight customers who call will have an incorrect address? (Round your answer to 4 decimal places.) |
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Probability |
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19.
Required information
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(d) |
What is the probability that fewer than nine customers who call will have an incorrect address? (Round your answer to 4 decimal places.) |
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Probability |
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20.
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If the weight (in grams) of cereal in a box of Lucky Charms is N(487,7), what is the probability that the box will contain less than the advertised weight of 457 gm? Note: You may need to use Excel to calculate the exact probabilities. (Round your answer to 5 decimal places.) |
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Probability |
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21.
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Automobile warranty claims for engine mount failure in a Troppo Malo 2000 SE are rare at a certain dealership, occurring at a mean rate of 0.37 claim per month. |
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(a) |
What is the probability that the dealership will wait at least 3 months until the next claim? (Round your answer to 4 decimal places.) |
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Probability |
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(b) |
What is the probability that the dealership will wait at least a year? (Round your answer to 4 decimal places.) |
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Probability |
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(c) |
What is the probability that the dealership will wait at least 2 year? (Round your answer to 4 decimal places.) |
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Probability |
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(d) |
What is the probability that the dealership will wait at least 3 months but not more than 1 year? (Round your answer to 4 decimal places.) |
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Probability |
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22.
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Answer the following: |
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a. |
Find the uniform continuous probability for P(X < 14) for U(0, 50). (Round your answer to 4 decimal places.) |
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Probability |
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b. |
Find the uniform continuous probability for P(X > 467) for U(0, 1,000). (Round your answer to 4 decimal places.) |
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Probability |
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c. |
Find the uniform continuous probability for P(19 < X < 56) for U(18, 63). (Round your answer to 4 decimal places.) |
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Probability |
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23.
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The credit scores of 35-year-olds applying for a mortgage at Ulysses Mortgage Associates are normally distributed with a mean of 630 and a standard deviation of 130. |
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(a) |
Find the credit score that defines the upper 10 percent. (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) |
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Credit score |
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(b) |
Sixty-five percent of the customers will have a credit score higher than what value? (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) |
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Credit score |
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(c) |
Within what range would the middle 70 percent of credit scores lie? (Use Excel or Appendix C for calculation of z-value. Round your final answer to 2 decimal places.) |
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Range |
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to |
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24.
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Between 11 p.m. and midnight on Thursday night, Mystery Pizza gets an average of 5.5 telephone orders per hour. |
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(a) |
Find the probability that at least 27 minutes will elapse before the next telephone order. (Round intermediate values and your final answer to 4 decimal places.) |
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Probability |
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(b) |
Find the probability that less than 20 minutes will elapse. (Round intermediate values and your final answer to 4 decimal places.) |
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Probability |
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(c) |
Find the probability that between 20 and 27 minutes will elapse. (Round intermediate values and your final answer to 4 decimal places.) |
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Probability |
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25.
If arrivals follow a Poisson distribution, waiting times follow the exponential distribution.
True
False
26.
For a continuous random variable, the total area beneath the PDF will be greater than zero but less than one.
True
False
[The following information applies to the questions displayed below.]
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Use the sample information |
27.
Required information
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(a) |
90 percent confidence. (Round your answers to 4 decimal places.) |
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The 90% confidence interval is from to |
28.
Required information
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(b) |
95 percent confidence (Round your answers to 4 decimal places.) |
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The 95% confidence interval is from to |
29.
Required information
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(c) |
99 percent confidence.(Round your answers to 4 decimal places.) |
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The 99% confidence interval is from to |
30.
Required information
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(d) |
Describe how the intervals change as you increase the confidence level. |
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The interval stays the same as the confidence level increases. |
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The interval gets wider as the confidence level increases. |
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The interval gets narrower as the confidence level increases. |
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The interval gets wider as the confidence level decreases. |
[The following information applies to the questions displayed below.]
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A random sample of 100 items is drawn from a population whose standard deviation is known to be σ = 50. The sample mean is |
31.
Required information
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(a) |
Construct an interval estimate for μ with 95 percent confidence. (Round your answers to 1 decimal place.) |
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The 95% confidence interval is from to |
32.
Required information
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(b) |
Construct an interval estimate for μ with 95 percent confidence, assuming that σ = 100. (Round your answers to 1 decimal place.) |
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The 95% confidence interval is from to |
33.
Required information
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(c) |
Construct an interval estimate for μ with 95 percent confidence, assuming that σ = 200. (Round your answers to 1 decimal place.) |
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The 95% confidence interval is from to |
34.
Required information
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(d) |
Describe how the confidence interval changes as σ increases. |
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The interval gets wider as σ increases. |
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The interval gets narrower as σ increases. |
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The interval gets wider as σ decreases. |
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The interval stays the same as σ increases. |
35.
In constructing a confidence interval for the mean, the z distribution provides a result nearly identical to the t distribution when n is large.
True
False
36.
As n increases, the width of the confidence interval will decrease, ceteris paribus.
True
False
37.
When the sample standard deviation is used to construct a confidence interval for the mean, we would use the Student's t distribution instead of the normal distribution.
True
False
38.
The Central Limit Theorem (CLT) implies that:
the population will be approximately normal if n ≥ 30.
the distribution of the mean is approximately normal for large n.
repeated samples must be taken to obtain normality.
the mean follows the same distribution as the population.
[The following information applies to the questions displayed below.]
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GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.21 mg of mercury. A sample of 50 bulbs shows a mean of 3.27 mg of mercury. |
39.
Required information
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(a) |
State the hypotheses for a right-tailed test, using GreenBeam’s claim as the null hypothesis about the mean. |
40.
Required information
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(b) |
Assuming a known standard deviation of 0.2 mg, calculate the z test statistic to test the manufacturer's claim. (Round your answer to 2 decimal places.) |
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Test statistic |
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41.
Required information
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(c) |
At the 10 percent level of significance (α = 0.1) does the sample exceed the manufacturer’s claim? |
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42.
Required information
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(d) |
Find the p-value. (Round your answer to 4 decimal places.) |
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p-value |
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43.
A simultaneous reduction in both α and β will require a larger sample size.
True
False
44.
The least squares regression line is obtained when the sum of the squared residuals is minimized.
True
False
45.
In a simple regression, if the coefficient for X is positive and significantly different from zero, then an increase in X is associated with an increase in the mean (i.e., the expected value) of Y.
True
False
46.
If R2 = .36 in the model Sales = 268 + 7.37 Ads, then Ads explains 36 percent of the variation in Sales.
True
False
47.
The ordinary least squares regression line always passes through the point .
True
False
48.
In simple linear regression, the coefficient of determination (R2) is estimated from sums of squares in the ANOVA table.
True
False
49.
A prediction interval for Y is narrower than the corresponding confidence interval for the mean of Y.
True
False
50.
When comparing the 90 percent prediction and confidence intervals for a given regression analysis:
the prediction interval is wider than the confidence interval.
the prediction interval is narrower than the confidence interval.
there is no difference between the size of the prediction and confidence intervals.
no generalization is possible about their comparative width.
51.
Which is not true of the coefficient of determination?
It is negative when there is an inverse relationship between X and Y.
It is calculated using sums of squares (e.g., SSR, SSE, SST).
It reports the percent of the variation in Y explained by X.
It is the square of the coefficient of correlation.
52.
A local trucking company fitted a regression to relate the cost of its shipments as a function of the distance traveled. The Excel fitted regression is shown.
Based on this estimated relationship, when distance increases by 50 miles, the expected shipping cost would increase by:
$143.
$301.
$286.
$104.
53.
If SSR is 2592 and SSE is 608, then:
the SST would be smaller than SSR.
the slope is likely to be insignificant.
the coefficient of determination is .81.
the standard error would be large.
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