Question

Suppose that Y has a binomial distribution with p = 0.40.

(a) Use technology and the normal approximation to the binomial distribution to compute the exact and approximate values of P(Y ≤ μ + 2)  for n = 5, 10, 15, and 20. For each sample size, pay attention to the shapes of the binomial histograms and to how close the approximations are to the exact binomial probabilities. (Round your answers to five decimal places.)

n = 5

exact value P(Y ≤ μ + 2) =

approximate value P(Y ≤ μ + 2)≈

n = 10

exact value P(Y ≤ μ + 2) =

approximate value P(Y ≤ μ + 2) ≈

n = 15

exact value P(Y ≤ μ + 2) =

approximate value P(Y ≤ μ + 2)≈

n = 20

exact value P(Y ≤ μ + 2)=

approximate value P(Y ≤ μ + 2)≈

Answer 1

As sample size increases graph of binomial distribution converges to normal distribution.

Complete solution is given in attached images:

Thank You.