Chapter 10.4, Problem 48E

Management training. Each year a company selects $5$ employees for a management training program at a university. On average, $40\%$ of those sent complete the course in the top $10\%$ of their class. If we consider an employee finishing in the top $10\%$ of the class a success in a binomial experiment, then for the $5$ employees entering the program, there exists a binomial distribution involving $P$ ( $x$ successes out of $5$ ).For the binomial distribution,

(A) Write the probability function.

(B) Construct a table.

(C) Draw a histogram.

(D) Compute the mean and standard deviation