Question

A random sample of 200 adults is taken from a population of 20000. It is believed that 86% of adults own a cell phone. Find the probability the sample proportion is between 84% and 87%

Answer 1

Solution:

Given that,

n = 200

= 86% =0.86

1 - = 1 - 0.86= 0.14

=   = 0.86

= ( 1 - ) / n

=   0.86 * 0.14 / 200

= 0.0245

= 0.0245

P( 0.84 < < 0.87 )  

P( 0.84 - 0.86 / 0.0474 ) < ( -    / ) < ( 0.87 - 0.86 / 0.0245 )

P ( - 0.02 /0.0245 < z < 0.01 / 0.0245 )

P ( -0.82 < z < 0.41)

P ( z < 0.41 ) - p ( z < -0.82 )

Using z table

= 0.6591 - 0.2061

= 0.4530

Probability = 0.4530