The owner of a car dealership is looking to model the number of purchases of vehicles. Let X be the number of purchases of vehicles in a single day, assuming that 95 customers arrive on that day. Historical data suggests that a customer will purchase a vehichle with probability 0.18. Answer the following questions and show all work, explaining each step.

a. What is the expected value of X?

b. What is the variance of X?

c. What is the probability that 13 cars are purchased on a single day?

d. What is the probability that 15 or fewer cars are purchased on a single day?

e. What is the probability that at least 20 cars are purchased on a single day?

f. What is the probability that less than 19 cars are purchased on a single day?

g. What is the probability that more than 21 cars are purchased on a single day?

h. What is the probability that the number of cars purchased on a single day is between 17 and 24 (inclusive of 17 and 24)?

i. What is the probability that the number of cars purchased on a single day is not strictly between 12 and 16?

j. What is the probability that 20 or more cars are purchased on a day?

k. Suppose that 17 cars are purchased on a day. What is the probability that 20 or more cars are purchased on a day?