Question 971479
8. An accountant is studying the time it takes a company to make payments on accounts payable. The mean time it takes to pay off an invoice is 13.8 days with a standard deviation of 4.3 days, and the times are normally distributed.

(a) What is the probability that an account is paid off in less than 16 days?
z(16) = (16-13.8)/4.3 = 2.2/4.3 = 0.5116
P(x < 16) = P(z<0.5116) = normalcdf(-100,0.5116) = 0.6955
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(b) Find the 95th percentile for the payoff time- that is, a time for which 95% of the accounts are paid off in less than that time.
Find the z-value with a right-tail of 0.95
invnorm(0.95) = 1.645
Find the corresponding time value::
x = 1.645*4.3+13.8 = 20.87
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(c) The company has just received 29 invoices. Find the probability that the mean payoff time for these invoices is more than 16 days.
t(16) = (16-13.8)/[4.3/sqrt(29)] = 2.7552
P(x > 16) = P(t> 2.7552 when df = 28) = tcdf(2.7552,100,28) = 0.005
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Cheers,
Stan H.
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