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.

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