# Basic Statistics and Probability

1. Owens Orchards sells apples in a large bag by weight. A sample of seven bags contained the following numbers of apples: 23, 19, 26, 17, 21, 24, 22.

a. Compute the mean number and median number of apples in a bag.

b. Verify that S (X - X) = 0.

2. The Citizens Banking Company is studying the number of times the ATM located in a Loblaws Supermarket at the foot of Market Street is used per day. Following are the numbers of times the machine was used over each of the last 30 days. Determine the mean number of times the machine was used per day.

83 64 84 76 84 54 75 59 70 61

63 80 84 73 68 52 65 90 52 77

95 36 78 61 59 84 95 47 87 60

3. The American Automobile Association checks the prices of gasoline before many holiday weekends. Listed below are the self-service prices for a sample of 15 retail outlets during the May 2003 Memorial Day weekend in the Detroit, Michigan, area.

1.44 1.42 1.35 1.39 1.49 1.49 1.41 1.46

1.41 1.49 1.45 1.48 1.39 1.46 1.44

a. What is the arithmetic mean selling price?

b. What is the median selling price?

c. What is the modal selling price?

4. recent article suggested that if you earn $25,000 a year today and the inflation rate continues at 3 percent per year, you'll need to make $33,598 in 10 years to have the same buying power. You would need to make $44,771 if the inflation rate jumped to 6 percent. Confirm that these statements are accurate by finding the geometric mean rate of increase.

5. The weights (in pounds) of a sample of five boxes being sent by UPS are: 12, 6, 7, 3, and 10.

a. Compute the range.

b. Compute the mean deviation.

c. Compute the standard deviation.

6. 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

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?

7. 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

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?

8. 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?

9 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?

10. 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?

See attached file for full problem description.

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#### Solution Summary

The solution gives details of computing basic statistics like Mean, Median, Mean Deviation, Standard Deviation and probability for a set of problems.