The brushes in the motors that control the conveyor belts at Delectable Delights need to be replaced periodically. Since there are many conveyor belts through the buildings, a supply of brushes is always kept on hand. The brushes come in shipments of 1000 from a supplier who claims that no more than 2% will be defective. Out of each shipment, a random sample of 15 brushes is selected for testing. If there are more than 1 defective brushes in the sample, the shipment will be rejected. Assume that all 15 brushes will be tested. Required:
a. Could the random variable X be considered a Binomial random variable?
b. Calculate the mean and standard deviation for X.