## Two six-sided dice are rolled and the random variable x is the sum of the values produced by each die.

### statistics

##### Description

Assignment #3

1.      Two six-sided dice are rolled and the random variable x is the sum of the values produced by each die.

a.       List the possible outcomes for the variable x, determine the probability for each outcome, and calculate the expected value of x.

b.      Calculate the variance of x.

c.       Calculate the standard deviation of x.

2.      Using historical records, a manufacturing firm has developed the following probability distribution for the number of days required to get components from its suppliers. The distribution is shown here, where the random variable x is the number of days.

 x 2 3 4 5 6 P(x) 0.15 0.45 0.3 0.075 0.025

a.       What is the average lead time for the component?

b.      What is the coefficient of variation for delivery lead time?

3.      A large corporation in search of a CEO and a CFO has narrowed the fields for each position to a short list. The CEO candidates graduated from Chicago (C) and three Ivy League universities: Harvard (H), Princeton (P),and Yale (Y). The four CFO candidates graduated from MIT (M), Northwestern (N), and two Ivy League universities: Dartmouth (D) and Brown (B). The personnel director wishes to determine the distribution of the number of Ivy League graduates who could fill these positions.

a.       Assume the selections were made randomly. Construct the probability distribution of the number of Ivy League graduates who could fill these positions.

b.      Would it be surprising if both positions were filled with Ivy League graduates?

c.       Calculate the expected value and standard deviation of the number of Ivy League graduates who could fill these positions.

4.      Hewlett-Packard receives large shipments of microprocessors from Intel Corp. It must try to ensure the proportion of microprocessors that are defective is small. Suppose HP decides to test five microprocessors out of a shipment of thousands of these microprocessors. Suppose that if at least one of the microprocessors is defective, the shipment is returned.

a.       If Intel Corp.’s shipment contains 10% defective microprocessors, calculate the probability the entire shipment will be returned.

b.      If Intel and HP agree that Intel will not provide more than 5% defective chips, calculate the probability that the entire shipment will be returned even though only 5% are defective

c.       Calculate the probability that the entire shipment will be kept by HP even though the shipment has 10% defective microprocessors

5.      Assume that for an ad campaign to be successful, at least 80% of those seeing a television commercial must be able to recall the name of the company featured in the commercial one hour after viewing the commercial. Before distributing an ad campaign nationally, an advertising company plans to show the commercial to a random sample of 20 people. It will also show the same people two additional commercials for different products or businesses.

a.       Assuming that the advertisement will be successful (80% will be able to recall the name of the company in the ad), what is the expected number of people in the sample who will recall the company featured in the commercial one hour after viewing the three commercials?

b.      Suppose that in the sample of 20 people, 11 were able to recall the name of the company in the commercial one hour after viewing. Based on the premise that the advertising campaign will be successful, what is the probability of 11 or fewer people being able to recall the company name?