Question

Of the households in a certain area, 40% have at least one compact automobile. A researcher selects a random sample of 84 households. That is the approximately probability that the proportion of households in the sample with at least one compact automobile is greater than 0.53?

Answer 1

Given,.

p = 0.40 , n = 84

Using central limit theorem,

P( < p) = P( Z < - p / sqrt( p (1 - p ) / n) )

So,

P( > 0.53) = P( Z > 0.53 - 0.40 / sqrt( 0.40 * 0.60 / 84) )

= P( Z > 2.4321)

= 1 - P( Z < 2.4321)

= 1 - 0.9925

= 0.0075