MAT201 Statistics

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MAT201BasicStatisticsModule3.docx
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Question 1 (3 points)

Compute the probability for a random variable X with µ=10 and σ=2. Calculate P(X<14).

Question 1 options:

A) 

0.8736

B) 

0.1586

C) 

0.9772

D) 

0.6827

Question 2 (3 points)

 

Suppose X ~ N (200, 10). This says that x is a normally distributed random variable with mean μ = 200 and standard deviation σ = 10. Suppose x = 170, calculate the z score.

Question 2 options:

A) 

3

B) 

-3

C) 

-1

D) 

2

Question 3 (3 points)

 

Suppose X has a normal distribution with mean 80 and standard deviation of 10. Between what values of x do 95% of the values lie?

Question 3 options:

A) 

60 and 90

B) 

60 and 100

C) 

75 and 85

D) 

50 and 110

Question 4 (3 points)

Suppose X ~ N (10, 6). This says that x is a normally distributed random variable with mean μ = 10 and standard deviation σ = 6. Suppose x = 20, then x= 20 means that it is:

Question 4 options:

A) 

1.67 below the mean

B) 

0.67 below the mean

C) 

0.67 above the mean

D) 

1.67 above the mean

Question 5 (3 points)

 

The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of five. What is the probability that a student scored more than 65% and less than 75% on the exam?

Question 5 options:

A) 

0.58

B) 

0.68

C) 

0.88

D) 

0.78

Question 6 (3 points)

To get admitted to top universities, the applicant's SAT (Scholastic Aptitude Test) score must be on a very high side. In terms of concepts learned in MAT201, this means that:

Question 6 options:

A) 

The applicant's SAT z-score has to be close to one.

B) 

The applicant's SAT z-score has to be negative.

C) 

The applicant's SAT z-score has to be positive and large.

D) 

The applicant's SAT z-score has to be close to zero

Question 7 (3 points)

If the z score=25, σ=2 and µ=50, what is x?

Question 7 options:

A) 

100

B) 

75

C) 

48

D) 

52

Question 8 (3 points)

The distribution of heights of adult American women is approximately normal with a mean of 64 inches and standard deviation of 2 inches. What percent of women is taller than 68 inches?

Question 8 options:

A) 

0.01

B) 

0.0014

C) 

0.05

D) 

0.025

Question 9 (3 points)

The final exam scores in a statistics class were normally distributed with a mean of 70 and a standard deviation of five. What is the probability that a student scored more than 75% on the exam?

Question 9 options:

A) 

0,84

B) 

0.95

C) 

0.16

D) 

0.68

Question 10 (3 points)

Compute the probability for a random variable X with µ=10 and σ=2. Calculate P(9 < X < 11).

Question 10 options:

A) 

0.3269

B) 

0.3565

C) 

0.3085

D) 

0.3829

Answer the following problems showing your work and explaining (or analyzing) your results.  Submit your work in a typed Microsoft Word document.

1. The final exam scores listed below are from one section of MATH 200.  How many scores were within one standard deviation of the mean? How many scores were within two standard deviations of the mean?

       99   34   86   57   73   85    91   93   46    96   88   79    68   85   89

2. The scores for math test #3 were normally distributed. If 15 students had a mean score of 74.8% and a standard deviation of 7.57, how many students scored above an 85%?

3. If you know the standard deviation, how do you find the variance?

4. To get the best deal on a stereo system, Louis called 8 out of 20 appliance stores in his neighborhood and asked for the cost of a specific model. Below is the sample data set of prices he collected:

       $216   $135   $281   $189   $218   $193   $299   $235

Find the standard deviation.

5. The Company collected a sample of the salaries of its employees. There are 70 salary data points summarized in the frequency distribution below:

Salary

Number of Employees

5,001–10,000

8

10,001–15,000

12

15,001–20,000

20

20,001–25,000

17

25,001–30,000

13

a. Find the standard deviation.

b. Find the variance.

6.  Calculate the mean and variance of the sample data set provided below. Show and explain your steps. Round to the nearest tenth.

       14,   16,   7,   9,   11,   13,   8,   10

7. Create a frequency distribution table for the number of times a number was rolled on a die. (It may be helpful to print or write out all of the numbers so none are excluded.)

    3,   5,   1,   6,   1,   2,   2,   6,   3,   4,   5,   1,   1,   3,   4,   2,   1,   6,   5,   3,   4,   2,   1,   3,   2,   4,   6,   5,   3,   1

8. Answer the following questions using the frequency distribution table you created in No. 7.

a. Which number(s) had the highest frequency?

b. How many times did a number of 4 or greater get thrown?

c. How many times was an odd number thrown?

d. How many times did a number greater than or equal to 2 and less than or equal to 5 get thrown?

9. The wait times (in seconds) for fast food service at two burger companies were recorded for quality assurance. Using the sample data below, find the following for each sample:

a. Range

b. Standard deviation

c. Variance

Lastly, compare the two sets of results.

Company

Wait times in seconds

Big Burger Company

105

67

78

120

175

115

120

59

The Cheesy Burger

133

124

200

79

101

147

118

125

10. What does it mean if a graph is normally distributed? What percent of values fall within 1, 2, and 3, standard deviations from the mean?

oSs_1512828

57081

57075

5

6

False

57089

7

1

57076

8

8

57083

False

9

57078

10

oSs_1512836