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. Complete parts a through e below. Number of orders 0 1 Probability 2 3 4 0.09 5 0.14 0.27 0.25 0.18 0.07 Let the random variable X represent numbers of new furnace orders that resulted from service calls in the last two weeks of September. a. Graph the probability distribution function. Choose the correct graph below. O A. O B. Q O c. O D 1-7 0.8- 0.6- 0.8- 0.4- * 0.6- Q 0.8- 2 0.6- 0.8- 8 0.6 0.2- . 0.4 0.2- 0.4- 0.2- 0.4- 0.2- 012345 012345 012345 012345 b. Calculate and graph the cumulative probability distribution F(x). Number of orders 0 2 3 4 5 P(x) 0.09 0.14 0.27 0.25 0.18 0.07 F (x ) (Type integers or decimals.)Choose the correct graph of F(x) below. O A. O B. O c. O D. 17 Q 17 Q Q 0.8- 20.6-] Q 0.8- x 0.6 0.8- 0.8- 0.4- 0.2- 0.4- 8 0.6- 0.2- 0.4- 0.6 0.4- 0.2- 0.2- 012345 012345 012345 01 012345 c. Find the probability that at least three orders will be generated in this period. (Type an integer or a decimal.) d. Find the mean of the number of orders for new furnaces in this 2-week period. (Type an integer or a decimal.) e. Find the standard deviation of the number of orders for new furnaces in this 2-week period. (Round to four decimal places as needed.)