4.19 A company specializes in installing and servicing central-heating furnaces. In the prewinter period, service calls may result in an order for a new furnace. The following table shows estimated probabilities for the numbers of new furnace orders generated in this way in the last two weeks of September.

Number of orders 0 1 2 3 4 5 Probability 0.10 0.14 0.26 0.28 0.30 0.05

a. Graph the probability distribution function.

b. Calculate and graph the cumulative probability distribution.

c. Find the probability that at least 3 orders will be generated in this period.

d. Find the mean of the number of orders for new furnaces in this 2-week period.

e. Find the standard deviation of the number of orders for new furnaces in this 2-week period.

Application Exercises