# Problems on Basic Probability

8.

A sample of 2,000 licensed drivers revealed the following number of speeding violations.

Number of Violations Number of Drivers

0 1,910

1 46

2 18

3 12

4 9

5 or more 5

Total 2,000

1. What is the experiment?

2. List one possible event.

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

4. 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:

Major

Gender Accounting Management Finance Total

Male 100 150 50 300

Female 100 50 50 200

Total 200 200 100 500

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

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

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

4. Are gender and major independent? Why?

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

6. 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?

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.

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

2. What percent of the garages take between 29 hours and 34 hours to erect?

3. What percent of the garages take 28.7 hours or less to erect?

4. 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.

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

2. What percent of the cruises will have 1,970 passengers or more?

3. What percent of the cruises will have 1,600 or fewer passengers?

4. 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

#### Solution Summary

This solution illustrates how to solve all of the above probability based problems in an attached Word document, including all of the calculations needed for these questions.