Question

Suppose a large shipment of microwave ovens contained 4% defectives. If a sample of size 362 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%? Round your answer to four decimal places.

Answer 1

Solution:

Given that,

n = 362

= 4% =0.04

1 - = 1 - 0.04 = 0.96

=   = 0.04

= ( 1 - ) / n

=   0.04 * 0.96 / 362

= 0.0103

= 0.0103

P (   < 0.03 )

P ( -    / ) < ( 0.03- 0.04 / 0.0103 )

P ( z < - 0.01 / 0.0103 )

Using z table

P ( z < -0.97 )

=0.1660

Probability = 0.1660