Question

A sample of 33 observations taken from an infinite population. The population proportion is .06, what is the probability that the sample proportion will be less than .1?

Answer 1

Using central limit theorem,

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

So,

P( < 0.10) = P( Z < 0.10 - 0.06 / sqrt( 0.06 * 0.94 / 33) )

= P( Z < 0.9676)

= 0.8334 (From Z table)