Question

According to​ research, 14​% of college women have been stalked. Use the normal approximation to the binomial to approximate the following probabilities for 95 college women selected at random.

a. What is the probability that the number of women who have been stalked is less than 13​? P(X < 13​) =

Answer 1

Solution :

Given that,

p = 0.14

q = 1 - p =1 -0.14 =0.86

n = 95

Using binomial distribution,

Mean = = n * p = 95*0.14=13.3

Standard deviation = = n * p * q =  95*0.14*0.86=3.3820

Using continuity correction ,

P(x< 12.5 ) = P((x - ) / < (12.5 -13.3) / 3.3820)

= P(z < -0.24)

Using z table

Probability = 0.0125