SOLUTION: An industrial firm allows a discount on any invoice that is paid within 30 days. it is known that 12% of all invoices recieve the discount. In a company audit 9 invoices are random

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Question 273271: An industrial firm allows a discount on any invoice that is paid within 30 days. it is known that 12% of all invoices recieve the discount. In a company audit 9 invoices are randomlu selected independent of each other. Let x be the number of invoices among the selected 9 that receive the discount.
a- find the probability that exactly 3 invoices amond these 9 receive the discount.
b- find the probability that at least one of the invoices receives a discount.
c- find the mean and standard deviation of x.
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
An industrial firm allows a discount on any invoice that is paid within 30 days.
It is known that 12% of all invoices receive the discount. In a company audit 9 invoices are randomly selected independent of each other.
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Binomial Problem with p = 0.12
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Let x be the number of invoices among the selected 9 that receive the discount.
a- find the probability that exactly 3 invoices among these 9 receive the discount.
P(x=3) = 9C3(0.12)^3(0.88)^6 = 0.0674
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b- find the probability that at least one of the invoices receives a discount.
P(at least one) = 1 - P(none receive a discount
P(at least one) = 1 - (0.88)^8
= 1 - 0.3165
= 0.6835
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c- find the mean and standard deviation of x.
mean = np = 9*0.12 =1.08
std = sqrt(npq) = 0.97488,,
Cheers,
Stan H.