Test #4 - Probability Distribution

Statistics

Tanaka

1. Let x be the number of homes sold per week by all four real estate agents working at a Century 21 office. The following table lists the probability distribution of x.

x 0 1 2 3 4 5

P(x) .15 .24 .31 .14 .10 .06

Calculate the mean and standard deviation of x. Give a brief interpretation of the value of the mean.

2. Johnson Electronics makes calculators. Consumer satisfaction is of the top priority of the company's management. The company guarantees a refund or a replacement for any calculator that malfunctions within 2 years from the date of purchase. It is known from the past that despite all efforts, 5% of the calculators manufactured by the company malfunctions within a two-year period. The company mailed a package of 10 randomly selected calculators to a store.

a. Let x denote the number of calculators in this package of 10 that will be returned for refund or replacement within 2-year period. Write the probability of distribution of x and draw a line graph of the probability distribution. Determine the mean and standard deviation of x.

b. Find the probability that exactly 2 of the 10 calculators will be returned for refund or replacement within a 2-year period.

3. Based on its analysis of the future demand for its products, the financial department at Tipper Corporation has determined that there is a .17 probability that the company will lose $1.2 million during the next year, a .21 probability that it will lose $0.7 million, a .37 probability that it will make a profit of $0.9 million, and a .25 probability that it will make a profit of $2.3 million.

a. Let x be the random variable that denotes the profit earned by this corporation during the next year. Write the probability distribution of x.

b. Find the mean and standard deviation of the probability distribution of part a. Give a brief interpretation of the value of the mean.

4. A box contains 10 parts, 3 of which are known to be defective. Suppose 2 parts are randomly selected from this box. Let x denote the number of good parts in this sample. Draw a complete tree diagram and use it to write the probability distribution of x. (Hint: Note that the draws are made without replacement from a small population. Hence, the probabilities of outcomes do not remain constant for each draw.)

5. According to a survey, 70% of adults believe that every college student should be required to take at least one course in ethics. Assume that this percentage is true for the current population of all adults.

a. Find the probability that the number of adults in a random sample of 12 who hold is

i. exactly 10

ii. at least 7

iii. less than 4

b. Let x be the number of adults in a random sample of 12 who believe that every college student should be required to take at least one course in ethics. Write the probability distribution of x. Find the mean and standard deviation of this probability distribution.

Subject | Mathematics |

Due By (Pacific Time) | 04062014 |

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