Question

Compute​ P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate this probability. If​ so, approximate​ P(X) using the normal distribution and compare the result with the exact probability. n= 62​, p= 0.4​, and X= 31

Answer 1

X = 31

n = 62

p = 0.4

Using binomial probability formula,

= 0.02847

Since, n * p = 24.8 > 10 and n * (1-p) = 37.2 > 10

So, X can be approximated by the normal distribution, with

Mean = np = 62 * 0.4 = 24.8

Variance = np(1-p) = 62 * 0.4 * (1-0.4) = 14.88

Standard deviation = √(14.88) = 3.86

So,

= 0.02845

Both the probabilities are approximately equal suggesting X is approximately normal.