Question

Dartmouth Distribution Warehouse makes deliveries of a large number of products to its customers. It is known that 76% of all the orders it receives from its customers are delivered on time. Let p^ be the proportion of orders in a random sample of 100 that are delivered on time. Find the probability that the value of p^ will be less than 0.80.

Round your answer to four decimal places.

Answer 1

Using central limit theorem

P($\hat{p}$ < p ) = P(Z < ($\hat{p}$ - p) / sqrt [ p( 1 - p) /n]

So,

P( $\hat{p}$ < 0.80) = P(Z < (0.80-0.76) / sqrt [ 0.76 ( 1 - 0.76) / 100 ]

= P(Z < 0.94)

= 0.8264