10% of all the items produced by a particular manufacturing process are defective. 400 randomly selected items were selected from a very large number of outputs.

Given that 400 items are randomly selected from a large number of outputs, they can be viewed as independent selections. In this case, let denotes the number of defective items out of these 400 selections. What distribution does follow? Write down the notation of this distribution.

a.Find [], () and the standard deviation of .

c. Can the distribution of be closely approximated by a normal distribution? Why or why not?

d. Suppose we are using a normal distribution to approximate the distribution of anyways. Find the probability that more than 58 items (out of the 400 selected ones) are defective.