Statistics: Various Probability Questions

Chapter 5

8. A sample of 2,000 licensed drivers revealed the following number of speeding violations.
Number of Violations Number of Drivers
0 1910
1 46
2 18
3 12
4 9
5 or more 5
Total 2000
a. What is the experiment?

b. List one possible event.

c. What is the probability that a particular driver had exactly two speeding violations?

d. What concept of probability does this illustrate?

66. A survey of undergraduate students in the School of Business at Northern University revealed
the following regarding the gender and majors of the students:

a. What is the probability of selecting a female student?

b. What is the probability of selecting a finance or accounting major?

c. What is the probability of selecting a female or an accounting major? Which rule of addition
did you apply?

d. Are gender and major independent? Why?

e. What is the probability of selecting an accounting major, given that the person selected
is a male?

f. Suppose two students are selected randomly to attend a lunch with the president of the
university. What is the probability that both of those selected are accounting majors?

Chapter 7

38. The accounting department at Weston Materials, Inc., a national manufacturer of unattached
garages, reports that it takes two construction workers a mean of 32 hours and a
standard deviation of 2 hours to erect the Red Barn model. Assume the assembly times follow
the normal distribution.

a. Determine the z values for 29 and 34 hours. What percent of the garages take between
32 hours and 34 hours to erect?

b. What percent of the garages take between 29 hours and 34 hours to erect?
c. What percent of the garages take 28.7 hours or less to erect?

d. Of the garages, 5 percent take how many hours or more to erect?

44. The number of passengers on the Carnival Sensation during one-week cruises in the
Caribbean follows the normal distribution. The mean number of passengers per cruise is
1,820 and the standard deviation is 120.

a. What percent of the cruises will have between 1,820 and 1,970 passengers?
b. What percent of the cruises will have 1,970 passengers or more

c. What percent of the cruises will have 1,600 or fewer passengers?
d. How many passengers are on the cruises with the fewest 25 percent of passengers?
60. In establishing warranties on HDTV sets, the manufacturer wants to set the limits so that
few will need repair at manufacturer expense. On the other hand, the warranty period must
be long enough to make the purchase attractive to the buyer. For a new HDTV the mean
number of months until repairs are needed is 36.84 with a standard deviation of 3.34
months. Where should the warranty limits be set so that only 10 percent of the HDTVs need
repairs at the manufacturer's expense?

The manufacturer of salad dressings uses machines to dispense the dressing into bottles that move along an assembly line. The machine is working well when 8 ounces is dispensed. The standard deviation of the process is 0.15 ounce. A sample of 50 bottles is selected periodically and the assembly line is stopped when there is evidence that the average amount dispensed is less than 8 ounces. Suppose that a sample of 50 bottles reveals an average of 7.983 ounces.

1. State the null and alternative hypotheses.
2. At the .05 level of significance, is there evidence that the average amount dispensed is less than 8 ounces?

A machine being used for packaging raisins has been set so that, on average, 15 ounces of raisins will be packaged per box. The operations manager wishes to test the machine setting and selects a sample of 30 consecutive raisin packages filled during the production process. The sample mean is 15.18 and the sample standard deviation is 0.4909. Use the t-distribution. Is there evidence that the mean weight per box is different from 15 ounces? (use level of significance equal to .05)