One of the toys made by Dillon Corporation is called Speaking Joe, which is sold only by mail. Consumer satisfaction is one of the top priorities of the company’s management. The company guarantees a refund or a replacement for any Speaking Joe toy if the chip that is installed inside becomes defective within 1 year from the date of purchase. It is known from past data that 10% of these chips become defective within a 1-year period. The company sold 15 Speaking Joes on a given day.
a. Let x denote the number of Speaking Joes in these 15 that will be returned for a refund or a replacement within a 1-year period. Using the appropriate probabilities table from Appendix C, obtain the probability distribution of x and draw a graph of the probability distribution. Determine the mean and standard deviation of x.
b. Using the probability distribution constructed in part a, find the probability that exactly 5 of the 15 Speaking Joes will be returned for a refund or a replacement within a 1-year period.