Question

AMC Inc. evaluates divisional managers in part by the number of consumer complaints senior management receives every month. The expectation is that no more than 20 complaints per division per month should be flagged for corporate attention. A sample of divisional data for the last five years or 60 months was collected. AMC defined X to be a random variable counting the number of complaints when twenty or more complaints in any division required senior management attention in a month; f(X) is the relative frequency of X. 30% of all complaints requiring corporate attention fell into this category and were included in the sample.

OPEN THE EXCEL EXAM TWO FILE. THE SPREADSHEET FOR THIS PROBLEM IS FOUND ON SHEET ONE. COMPLETE AND SAVE YOUR WORK IN EXCEL AND ENTER THE SOLUTIONS BELOW.

1. (5 points) What is the probability that X = 21? In one sentence, explain how you know.

Answer 1

BIONOMIAL DISTRIBUTION
pmf of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
I.
mean = np
where
n = total number of repetitions experiment is executed
p = success probability
mean = 60 * 0.3
= 18
II.
variance = npq
where
n = total number of repetitions experiment is executed
p = success probability
q = failure probability
variance = 60 * 0.3 * 0.7
= 12.6
III.
standard deviation = sqrt( variance ) = sqrt(12.6)
=3.5496

a.
the probability that X = 21
P( X = 21 ) = ( 60 21 ) * ( 0.3^21) * ( 1 - 0.3 )^39
= 0.076