Reference no: EM132857030

1) A company that sells binders decides to run a promotion on their 1-inch and 2-inch size binders. They discount the 1-inch binders to $1 per binder and discount the 2-inch binders to $2 per binder. They limit sales to a quantity of 5 of each size of binder per customer. The probability distribution of "X = the number of 1-inch binders purchased by a single customer during the promotion period" is given in the table below. X 1 2 3 4 5 P(X) 0.02 0.09 0.12 0.15 0.62

a) Compute the mean and standard deviation of X.

b) The company's cost of manufacturing a single 1-inch binder is $0.25. What is the expected profit (in dollars) that the company will make, per customer, for 1-inch binder sales during the promotion?

c) The mean and standard deviation of "Y = the number of 2-inch binders purchased by a single customer" is 2.74 and 1.25, respectively. Assume that the number of 1-inch and 2-inch binders purchased are independent random variables. What are the mean and standard deviation of the total number of binders purchased by a single customer?

d) The company's cost of manufacturing a single 2-inch binder is $0.55. What is the total expected profit (in dollars) that the company will make, per customer, during the promotion?

2) To celebrate the opening of a new store, when a customer gets to the register, they get to spin a prize wheel that is equally divided into 4 parts. Depending on what part the customer lands on, they win either a 10%, 20%, 30%, or 50% discount on their entire purchase.

a) What is the probability that the first customer to win a 50% discount is the 5th customer to get to the register?

b) What is the probability that at least 3 of the first 5 customers win a discount of at least 30%?

c) At the end of the day, the records show that 140 customers made a purchase at the store that day. What are the mean and standard deviation of the number of customers who won a discount of at least 30%?