Question

According to a survey in a country, 47​% of adults do not have any credit cards. Suppose a simple random sample of 400 adults is obtained.

• What is the probability that 195 or more have no credit cards?

Answer 1

Given that,

p = 0.47

q = 1 - p = 1 - 0.47 = 0.53

n = 400

Using binomial distribution,

= n * p = 400 * 0.47 = 188

= n * p * q = 400 * 0.47 * 0.53 = 9.982

Using continuity correction ,

P(x 195 - 0.5) = P( x 194.5 )

= 1 - P(x   194.5)

= 1 - P((x - ) / (194.5 - 188) / 9.982)

= 1 -  P(z 0.65)  

= 1 - 0.7422

= 0.2578

Probability = 0.2578