Statistical Analysis of Probabilities in Real-Life Situations

1.) A recent survey by the American Accounting Association revealed 23 percent of students graduating with a major in accounting select public accounting. Suppose we select a sample of 15 recent graduates.

a. What is the probability two select public accounting?
b. What is the probability five select public accounting?
c. How many graduates would you expect to select public accounting?

2.) Keith's Florists has 15 delivery trucks, used mainly to deliver flowers and flower arrangements in the Greenville, South Carolina, area. Of these 15 trucks, 6 have brake problems. A sample of 5 trucks is randomly selected. What is the probability that 2 of those tested have defective brakes?

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1. Sixty percent of the customers of a fast food chain order the Whopper, french fries and a drink. If a random sample of 15 cash register receipts is selected, what is the probability that 10 or more will show that the above three food items were ordered?
A. 1,000
B. 0.186
C. 0.403
D. 0.000
E. None of the above

2. Judging from recent experience, 5 percent of the worm goes produced by an automatic, high- speed machine are defective. What is the probability that out of six gears selected at random, exactly zero gears will be defective?
A. 0.001
B. 0.167
C. 0.735
D. 0.500
E. None of the above

Questions 3-5;
David's gasoline station offers 4 cents off per gallon if the customer pays cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one hour period twenty-five customers buy gasoline at this station.

3. What is the probability that at least ten pay in cash?
A. 0.416
B. 0.575
C. 0.586
D. 0.425
E. None of the above
4. What is the probability that no more than twenty pay in cash?
A. 0.0
B. 0.1
C. 0.9
D. 1.0
E. None of the above

5. What is the probability that more than ten and less than fifteen customers pay in cash?
A. 0.541
B. 0.401
C. 0.380
D. 0.562
E. None of the above

Questions 6-8:
Affirmative action commitments by industrial organizations have led to an increase in the number of women in executive positions. Satellite Office Systems has vacancies for two executives which it will fill from among four women and six men.

6. What is the probability that no woman is selected?
A. 1/5
B. 1/3
C. 2/15
D. 8/15
E. None of the above

7. What is the probability that at least one woman is selected?
A. 8/15
B. 3/5
C. 2/3
D. ¾
E. None of the above

8. What is the probability that exactly one woman is selected?
A. 1/5
B. 1/3
C. 2/15
D. 7/15
F. 8/15

Questions 9-11
A statistic professor finds she averages five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution.

9. What is the probability that on a randomly selected day she will have no messages?
A. 0.0067
B. zero
C. 0.0335
D. Impossible to have no messages
E. None of the above

10. What is the probability that on a randomly selected day she will have five messages?
A. 0.0067
B. 0.875
C. 0.175
D. 1.0
E. None of the above

11. What is the probability that on a randomly selected day she will have two messages?
A. 0.0067
B. 0.0014
C. 0.420
D. 0.084
E. None of the above

Questions 12-18:
A loaf of bread is normally distributed with a mean of 22 ounces and a standard deviation of ½ ounces.

12. What is the probability that a loaf of bread is <20 ounces?
A. 7
B. 3
C. 2
D. 1
E. 5

13. What is the probability that a loaf of bread is >21 ounces?
A. 0.4689
B. 0.8941
C. 0.0214
D. 0.9772
E. 0.8523

14. What is the probability that a loaf of bread is >23 ounces?
A. 0.0874
B. 0.9102
C. 0.6651
D. 0.5987
E. 0.0228

15. What is the probability that a loaf of bread is <24 ounces?
A. 1.065
B. 1.0
C. 0.331
D. 0.715
E. 0.815

16. What is the probability that a loaf of bread is between 20.75 and 23.25 ounces?
A. 0.9876
B. 0.2115
C. 0.9015
D. 0.5879
E. 0.9687

17. What is the probability that a loaf of bread is 22.25 ounces?
A. 0.3085
B. 0.0112
C. 0.9854
D. 0.6598
E. 0.3077

18. What is the probability that a loaf of bread is between 21.75 and 22.25 ounces?
A. 0.4679
B. 0.3918
C. 0.5931
D. 0.2125
E. 0.3830

Questions 19-20:
Two business major students, in two different sections of economics, were comparing test scores. The following gives the students scores, class mean, and standard deviation for each section.
Section Score &#61549; &#61555;
1 84 75 7
2 75 60 8

19. Which student scored better compared to the rest of the section?
A. Section 1 or 2
B. None of the sections
C. Scores more than 75
D. Scores less than 83
E. None of the above

20. What is the z-score of the student from section 1?
A. 0.51
B. 0.47
C. 0.02
D. 0.15
E. None of the above

Questions 21-23:
The average score of 100 students taking a statistics final was 70 with a standard deviation of 7.

21. Assuming a normal distribution, approximately how many scored 90 or higher?
A. 0.4979
B. 0.0021
C. 0.9979
D. 2.86
E. None of the above

22. Assuming a normal distribution, approximately how many scored less than 60?
A. 0.2271
B. 0.3729
C. 0.8929
D. -1.14
E. None of the above

23. Assuming a normal distribution, approximately how many scored greater than 65?
A. 0.2611
B. 0.2389
C. 0.7611
D. -0.714
E. None of the above