Answer)
3)
As the population s.d is given we can use standard normal z table to estimate the answer
Z = (x-mean)/s.d
Given mean = 16
S.d = 5
A)
Filtration system will require warranty repair if, x< 10
P(x<10)
Z = (10 - 16)/5
Z = -1.2
From z table, p(z<-1.2) = 0.1151
Required probability is 0.1151
B)
Probability that a system requires repairing = 0.1151
So total number of systems which requires repairing = 0.1151*1000 = 115.1
Profit when a system requires repair = 300-50 = $250
And profit when a system does not require repair = $300
Profit for 115.1 (systems which requires repair) = 28775 (115.1*250)
Profit for 1000 - 115.1 = 884.9 (systems which does not require repair) =
265470
Total expected profit = 265470 + 28775
= $294245
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