To increase sales, a local donut shop began putting an extra donut in some of the boxes. Customers are unaware of which boxes had the extra donut and the shop owner claimed that one in seven boxes had an extra donut. Eight customers each bought one box of donuts at the shop. Let X = the number of customers that bought a box containing an extra donut.

Part A:Is X a binomial random variable? Explain. (3 points)

Part B:What is the mean and standard deviation of X? Provide an interpretation for each value in context. (4 points)

Part C:Two of the eight customers buy a box of donuts with an extra donut. Is the shop's claim accurate? Compute P(X 2) and use the result to justify your answer. (3 points)

Please explain the work and show calculator imputs