Descriptive Statistics and Probability Calculation

Please show all work.

1. There are 10 rolls of film in a box and 3 are defective. Two rolls are to be selected, one after the other (without replacement). What is the probability that neither roll will be defective?

2. The Ace Battery Company manufactures automobile batteries. The company has determined that the lives of its batteries are normally distributed with a mean life (u) of 52 months with a population standard deviation (sigma) of 3 months. If someone purchases one of their batteries, what is the probability that it will last:
a. longer than 56 months?
b. less than 52 months?

3. A board of directors consists of 8 men and 4 women. A four-member search committee is to be chosen at random to recommend a new company president. What is the probability that all 4 members of the search committee will be women?

4. Non-resident annual fees for a sample of accredited U.S. senior colleges and universities are:
Adelphi U. $ 3,510 U. of Detroit $ 3,450
U. of Alabama 1,543 Eastern Kentucky U. 1,200
Alcorn State U. 784 U. of Florida 1,710
Bates College 4,850 Knox College 3,795
Brigham Young U. 1,350 New Hampshire Coll. 3,692
Carleton College 5,725 U. of Rhode Island 2,125

a. Determine the median annual fees.
b. Determine the mode of the annual fees.
c. Determine the standard deviation of the annual fees.
d. Construct a frequency table of the annual fees using 4 classes.
e. Construct a histogram of the frequency table in (g).

5. In a management training program 80 of the trainees are female and 20 are male. Seventy-two of the females attended college and 16 of the males attended college. If one trainee is selected at random, what is the probability that this trainee will be either a college graduate or a male?

6. A manufacturing process produces products that are defective 4% of the time. If samples are taken of 15 products at a time, what is the probability that in a given sample there will be 5 defective parts?

7. Keyes Home Furnishings ran six local newspaper advertisements during December. The following frequency distribution resulted:

Number of times subscriber
saw ad during December 0 1 2 3 4 5 6
Frequency (# subscribers) 897 1,082 1,325 814 307 253 198

What is the average number of times a subscriber saw a Keyes advertisement during December?