Question

A random sample of size 144 is taken from a population described by the proportion p = 0.75. The probability that the sample proportion is greater than 0.72 is ________.

Answer 1

Solution

Given that,

p = 0.75

1 - p = 1 -0.75=0.25

n = 144

= p =0.75

=  [p( 1 - p ) / n] = [(0.75*0.25) / 144 ] = 0.036

P( > 0.72) = 1 - P( < 0.72)

= 1 - P(( - ) / < (0.72-0.75) / 0.036)

= 1 - P(z <-0.83 )

Using z table

= 1 -0.2033

=0.7967

probability=0.7967