1) An agency collects demographics concerning the number of people in families per household in a certain country. Assume the distribution of the number of people per household is as shown in the table

x P(x)

2 0.29

3 0.21

4 0.30

5 0.13

6 0.05

7 0.03

a. Calculate the expected number of people in families per household in the country.

b. Compute the standard deviation of the number of people in families per household.

2) A consumer electronics store stocks 6 alarm clock radios. If it has fewer than6 clock radios available at the end of aweek, the store restocks the item to bring thein-stock level up to6. If weekly demand is greater than the 6 units instock, the store loses sales. The radio sells for$26and costs the store$13. The manager estimates that the probability distribution of weekly demand for the radio is as shown in the provided data table. Complete parts a through d below.

Weekly Demand Probability

0 0.04

1 0.06

2 0.08

3 0.19

4 0.32

5 0.14

6 0.08

7 0.07

a. What is the expected weekly demand for the alarm clockradio?

b. What is the probability that weekly demand will be greater than the number of availableradios?

c. What is the expected weekly profit from the sale of the alarm clockradio? (Remember: There are only6 clock radios available in any week to meetdemand.)

d. Onaverage, how much profit is lost each week because the radio is not available whendemanded?