A computer supply house receives a large shipment of flash drives each week. Past experience has shown that the number of flaws (bad sectors) per flash drive is either 0, 1, 2, or 3 with probabilities .65, .2, .1, and .05, respectively.

a. Calculate the mean and standard deviation of the number of flaws per flash drive.

b. Suppose that we randomly select a sample of 100 flash drives. Describe the shape of the sampling distribution of the sample mean. Then compute the mean and the standard deviation of the sampling distribution of .

c. Sketch the sampling distribution of the sample mean and compare it to the distribution describing the number of flaws on a single flash drive.

d. The supply house’s managers are worried that the flash drives being received have an excessive number of flaws. Because of this, a random sample of 100 flash drives is drawn from each shipment and the shipment is rejected (sent back to the supplier) if the average number of flaws per flash drive for the 100 sample drives is greater than .75. Suppose that the mean number of flaws per flash drive for this week’s entire shipment is actually .55. What is the probability that this shipment will be rejected and sent back to the supplier?