Online Teleshopping appliances sells 10 dishwashers each week. Twenty percent of all purchasers of dishwashers buy an extended warranty. Let the random variable X denote the number of the next 10 purchasers in a week who buy extended warranty. 

 

a$)$ Identify the distribution of the random variable X$.$ 

 

b$)$ Find mean and standard of purchases. 

 

c$)$ Find the probability that no one takes warranty. 

 

d$)$ Find the probabilities that two, three, four purchasers tale the warranty