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

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