Question

If x is a binomial random variable with n = 20, and p = 0.30, then p(x = 10) = 0.50.
a. True
b. False

Answer 1

In the binomial expansion of (0.30+0.70)²⁰ the coefficient is ²⁰C₁₀=184756 for x=10 and we have 0.30¹⁰×0.70¹⁰ for the pq values where q=1-p. This comes to about 0.03. So the statement p(x=10)=0.50 is false, answer b.