A computer supply house receives a large shipment of blank CDs each week. Past experience has shown that the number of flaws per CD can be described by the following probability distribution, where the random variable X represents the number of flaws per CD.
x
P(X = x)
0
0.65
1
0.20
2
0.10
3
0.05
(A) Calculate the mean and standard deviation of the number of flaws per CD.
(B) Suppose you select two CDs at random. What is the sampling distribution of the average number of flaws on the two CDs? That is, what is the sampling distribution of the sample mean X ?
(C) Suppose you select 100 CDs at random. What is the (approximate) sampling distribution of the sample mean X? Why?
(D) Suppose you select 100 CDs at random. Approximate the probability that the sample mean Xis less than 0.4.