Question

If a random sample of 100 items is taken from a population in which the proportion of items having a desired attribute is p=0.30, what is the probability that the proportion of successes in the sample will be less than or equal to 0.33?

Answer 1

Solution

Given that,

p = 0.30

1 - p = 1 - 0.30 = 0.70

n = 100

= p = 0.30

=  p ( 1 - p ) / n

=   (0.30 * 0.70) / 100 = 0.0458

P( 0.33) =

= P(( - ) / < (0.33 - 0.30) / 0.0458)

= P(z < 0.655)

= 0.7438

Probability = 0.7438