Question

Suppose 44% of the children in a school are girls. If a sample of 545 children is selected, what is the probability that the sample proportion of girls will be less than 43% ? Round your answer to four decimal places.

Answer 1

Solution

Given that,

p = 44% = 0.44

1 - p = 1 - 0.44 = 0.56

n = 545

= p = 0.44

=  [p ( 1 - p ) / n] =   [(0.44 * 0.56) / 545 ] = 0.0213

P( < 0.43 )

= P[( - ) / < ( 0.43 - 0.44 ) / 0.0213 ]

= P(z < -0.47 )

Using z table

= 0.3192