General Electric (GE) appliances come with a traditional warranty, but the company also offers extended coverage with a Service Protection Advantage plan from Assurant, GE's authorized provider of extended warranties

General Electric (GE) appliances come with a traditional warranty, but the company also offers extended coverage with a Service Protection Advantage plan from Assurant, GE's authorized provider of extended warranties. The plan covers parts and labor for appliance repairs for an extended period. According to data compiled by Assurant, thirty percent of consumers who purchase a new GE appliance also buy the Service Protection Advantage plan.

Assume that a random sample of fourteen consumers who purchased a new GE appliance is drawn. Let us define X to be a binomial random variable representing whether or not a consumer purchased the Service Protection Advantage plan with their new GE appliance purchase this year.

a) What is the probability that no more than six of the sampled consumers purchased the Service Protection Advantage plan with their new GE appliance? ______

b) What is the probability that at least seven, but less than ten, of the sampled consumers purchased the Service Protection Advantage plan with their new GE appliance? ______

c) If you were to take repeated random samples of fourteen consumers who purchased a new GE appliance, what is the average number of them you would expect to also purchase the Service Protection Advantage plan? ______