A1 Dealership settles 75 of complaints it receives involving

A1 Dealership settles 75% of complaints it receives involving new car dealers. Suppose a sample of 120 complaints involving new car dealers is selected. Find the probability that A1 Dealership settles less than 104 of these complaints

Solution

prob of success , p= 0.75

n = 120 , which is very large

So, normal approximation is done accordingly.

mean = n * p = 120 * .75 = 90

std dev. = sqrt(n * p * (1-p) ) = sqrt(120 * .75 * .25) = 4.7434

P(X<104) = P( (X - mean)/std dev < (104 - 90)/4.7434 )

                = P(Z < 2.95)

                = 0.9984 (ANS)