This practice exam consists of 25 multiple choice questions and is similar (in format, types of questions, etc.) to the exam you will take for credit. The time limit for all module exams is 2 hours. It is recommended that you take this practice exam under exam conditions in order to prepare for the module exam. When you are finished with the exam you can check your answers by clicking here.  The module exams are worth 100 points (4 points per question).
 

The next two questions refer to the following situation. Suppose the amount of time it takes the Internal Revenue Service (IRS) to send refunds to taxpayers is normally distributed with a mean of 12 weeks and standard deviation of 3 weeks.

1.) What percentage of taxpayers should get a refund within 6 weeks?

a. 97.72%
b. 24.86%
c. 25.14%
d. 47.72%
e. 2.28%

2.) What percentage of taxpayers will have to wait between 9 and 15 weeks?

a. 34.13%
b. 12.93%
c. 68.26%
d. 25.86%
e. 99.70%
 

The next three questions refer to the following situation.  Suppose we have an urn that contains 10 balls.  There are 4 red balls number 1, 2, 3, and 4 and 6 green balls number 5, 6, 7, 8, 9, and 10.  For the purpose of the next three questions, the experiment consists of randomly selecting one ball from the urn.

3.) What is the probability of selecting an even numbered green ball?

a. 0.20
b. 0.60
c. 0.50
d. 0.30
e. 0.83

4.) What is the probability of selecting an odd numbered ball given that the ball is red?

a. 0.50
b. 0.25
c. 0.40
d. 0.20
e. 0.70

5.) Consider the following two events:  RED = {select a red ball at random} and ODD = {select a ball with an odd number}.  Which of the following statements is true?

a. RED and ODD are mutually exclusive events
b. RED and ODD are dependent events
c. RED and ODD are both dependent and mutually exclusive
d. RED and ODD are independent events
e. RED and ODD are both independent and mutually exclusive
 

Use the following information to answer the next two questions.  In the biathlon event of the Olympic Games, a participant skis cross-country and on four intermittent occasions stops at a riflerange and shoots a set of five shots.  If the center of the target (bull's eye) is hit, no penalty points are assessed.  Suppose a particular man has a history of hitting the bull's eye with 90% accuracy.

6.) What is the probability that he will hit the bull's eye on at least four of his next set of five shots?

a.  0.4095
b.  3.6000
c.  0.3281
d.  0.5905
e.  0.9185

7.) On average, how many bull's eyes will he hit on a set of five shots?  Also, what is the standard deviation of the number of bull's eyes the man hits on a set of five shots (respectively)?

a.  0.5, 0.4500
b.  4.5, 0.4500
c.  0.5, 0.6708
d.  4.5, 0.6708
e.  4.5, 2.1213
 

The next three questions refer to the following situation. The average "checkout" receipt at a large supermarket is $65 with a standard deviation of $21. Suppose random samples of 45 "checkout" receipts are taken for observation.

8.) What is the standard error of the mean?

a. 0.47
b. 9.80
c. 21.00
d. 3.13
e. 32.31

9.) What is the probability that a sample average will fall below $70?

a. 0.5948
b. 0.4452
c. 0.9452
d. 0.8621
e. 0.0548

10.) There is a 95% chance that the sample mean will fall below how many dollars?

a. $59.85
b. $71.13
c. $99.55
d. $81.12
e. $70.15
 

Answer the next two problems based on this situation. Daily sales of television sets at a local department store follow a normal
distribution, with a mean of $1890, and a standard deviation of $550.

11.) What is the probability that the sales for a given day will be less than $1600?

a. .7019
b. .2981
c. .2019
d. .5273
e. none of the above

12.) We would expect daily sales to exceed what amount on 80% of the days (Hint:  This is the 20^th percentile.)?

a. $550
b. $2352
c. $1890
d. $1428
e. $2330
 

The next two questions refer to the following situation.  Prescott National Bank has six tellers available to serve customers.  The number of tellers busy with customers at, say, 1:00 P.M. varies from day to day and depends on chance; so it is a random variable, which we will call X.  Past records indicate that the probability distribution of X is as shown in the following table.
 

We see, for example, that the probability is 0.262 that exactly five of the tellers will be busy with customers at 1:00 P.M.  For the next two questions the experiment consists of observing the number of busy tellers at 1:00 P.M. on a randomly selected day.

13.) What is the probability that at least 2 tellers will be busy at 1:00 P.M.?

a. 0.844
b. 0.078
c. 0.922
d. 0.156
e. 0.571

14.) How many tellers can you expect to be busy at 1:00 P.M.?

a. 3.240
b. 3.000
c. 3.500
d. 2.480
e. 4.118
 

15.) According to the Central Limit Theorem, which of the following statements is true?

a. The mean of all sample means is proportional to n.
b. The mean of all sample means is inversely proportional to the square root of n.
c. The mean of all sample means is inversely proportional to n.
d. The mean of all sample means is proportional to the square root of n.
e. The mean of all sample means is the same as the population mean.
 

The next three questions refer to the following situation.  The U.S. National Center for Education Statistics compiles information on institutions of higher education and publishes its findings in Digest of Education Statistics.  Following is a contingency table giving the number of institutions of higher education in the United States by region and type.  For the purpose of the next three questions, the experiment consists selecting one of these 3,274 institutions at random.
 

16.) What is the probability that the institution is from the West?

a. 0.1695
b. 0.5640
c. 0.4360
d. 0.4331
e. 0.2041

17.) What is the probability of selecting a private Midwestern institution?

a. 0.1452
b. 0.1890
c. 0.8143
d. 0.4786
e. 0.1539

18.) What is the probability of selecting a private institution given that the institution is from the Northeast?

a. 0.6760
b. 0.1695
c. 0.3078
d. 0.1381
e. 0.5507
 

The next two questions refer to the following situation. Sales of peanuts (in bulk) are normally distributed with a mean of 18 ounces and a standard deviation of 2 ounces.

19.) What is the probability that the next customer will purchase at least 15 ounces of peanuts in bulk?

a. 0.4332
b. 0.7734
c. 0.0668
d. 0.9332
e. 0.5668

20.) What is the median number of ounces purchased?

a. 50.0
b. 20.0
c. 18.0
d. 17.0
e. 19.0
 

The next two questions refer to the following situation. Suppose that, in manufacturing, the probability of a certain item being defective is 0.25. An inspector randomly selects 6 items for testing.

21.) What is the probability that the inspector finds at least one defective item?

a. 0.8220
b. 0.4660
c. 0.3560
d. 0.5340
e. 0.1780

22.) What is the probability that the inspector finds at most one defective item?

a. 0.4660
b. 0.8220
c. 0.5340
d. 0.3560
e. 0.1780
 

The next two questions refer to the following situation. A dentist knows that the mean elapsed time between regular checkups for her
patients is 8.4 months with a standard deviation of 2.4 months. Suppose a group of 36 of her patients is randomly selected.

23.) What is the probability that the sample mean for elapsed time between office visits is between 8 and 9 months?

a. 0.7745
b. 0.2255
c. 0.1662
d. 0.9937
e. 0.4332

24.) Within what limits around the population mean can we be 60% certain that the sample mean will fall?

a. (7.892, 9.186)
b. (8.266, 8.534)
c. (8.344, 8.456)
d. (8.064, 8.736)
e. (6.384, 10.416)
 

25.) What is the area under the standard normal curve that lies to the right of -1.07?

a. 0.6423
b. 0.8577
c. 0.9554
d. 0.0446
e. 0.3577

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