Chapter 10, Problem 11RE

In Problems 10 and 11, discuss the validity of each statement. If thestatement is always true, explain why. If not, give a counterexample.

(A) If $X$ represents a binomial random variable with mean $\mu$, then $P\left(X\ge \mu \right)=.5$

(B) If $X$ represents a normal random variable with mean $\mu$ then $P\left(X\ge \mu \right)=.5$.

(C) The area of a histogram of a binomial distribution is equal to the area above the x axis and below a normal curve.