Suppose 10% of the tubes produced a machine are defective. If a sample of 100 tubes is inspected at random, find the following.

a) The expected proportion of defective in the sample.

b) The variance of the proportion of defective in the sample.

c) The approximate distribution of the sample proportion.

d) The probability that the proportion of defective will exceed 0.16.

e) The probability that the number of defective will be at most 32.