# 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?

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#### Solution Summary

The solution provides step by step method for the calculation of descriptive statistics and probability. Formula for the calculation and Interpretations of the results are also included.

In a poll, respondents were asked whether they had ever been in a car accident

Solve the following problems showing your work:

1. In a poll, respondents were asked whether they had ever been in a car accident. 157 respondents indicated that they had been in a car accident and 117 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident?

2. The data set represents the income levels of the members of a country club. Find the probability that a randomly selected member earns at least $88,000

108000 128000 82000 138000 85000 10800 88000 76000 158000 208000

79000 98000 148000 85000 128000 118000 88000 168000 73000 118000

3. In a certain class of students, there are 15 boys from Wilmette, 5 girls from Kenilworth, 9 girls from Wilmette, 6 boys from Glencoe, 2 boys from Kenilworth and 8 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?

4. Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 5 possible answers.

5. Of 1936 people who came into a blood bank to give blood, 220 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

Use information from the modular background readings as well as any good quality resource you can find. Please cite all sources and provide a reference list at the end of your paper.

The following items will be assessed in particular:

1. Identify the meaning of independent and dependent events.

2. Calculate probabilities and joint probabilities of simple events.

3. Explain the basic logic of probability theory

Solve the following problems showing your work (Measures of Central Tendency)

1. Last year, nine employees of an electronics company retired. Their ages at retirement are listed below. Find the mean retirement age.

57 62 62

55 66 58

65 50 50

2. A store manager kept track of the number of newspapers sold each week over a seven-week period. The results are shown below.

36 30 201 180 278 242 310

Find the median number of newspapers sold.

3. Last year, nine employees of an electronics company retired. Their ages at retirement are listed below.

52 65 67 51 60 64 68 58 56 Find the Mode

4. The amount of time (in hours) that Sam studied for an exam on each of the last five days is given below. Find the mean study time.

3.7 8.2 8.7 6.4 4.6

5. The distances (in miles) driven in the past week by each of a company's sales representatives are listed below.

45 70 242 268 452 490 640

Find the median distance driven.

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