Question

Let x be a binomial random variable with n = 25 and the probability of failure is 0.4. Using the normal distribution to approximate the binomial, determine the probability that more than 12 successes will occur.

A. 0.8461

B. 0.1539

C. 0.9192

D. 0.0329

Answer 1

Solution :

Given that,

Using binomial distribution,

= n * p = 25 * 0.4 = 10

= n * p * q = 25 * 0.4 * 0.6 = 2.4495

Using continuity correction ,

P(x > 12.5) = 1 - P(x < 12.5)

= 1 - P((x - ) / < (12.5 - 10) / 2.4495)

= 1 - P(z < 1.02)

= 1. - 0.8461

= 0.1539

Probability = 0.1539

Option B) is correct .