Question

Suppose a large shipment of microwave ovens contained 14% defectives. If a sample of size 278 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 5%? Round your answer to four decimal places.

Answer 1

Solution :

Given that ,

p = 14% = 0.14

1 - p = 1- 0.14 = 0.86

n = 278

= p = 0.14

= (p*(1-p))/n =  (0.14*0.86)/278 = 0.02081

P(0.09 < < 0.19)

P(0.9 < <0. 19) = P((0.9-0.14)/0.02081 ) < ( - ) /  < (0.19-0.14) /0.02881 ) )

= P(-2.403 < z < 2.403 )

= P(z < 2.403) - P(z < -2.403)

= 0.9919 - 0.0081

= 0.9838

Probability = 0.9838