Question 1076085: Express Courier Service has found that the delivery time for packages is normally distributed, with mean 15 hours and standard deviation 2 hours.
(a) For a package selected at random, what is the probability that it will be delivered in 18 hours or less? (Round your answer to four decimal places.)
(b) What should be the guaranteed delivery time on all packages in order to be 95% sure that the package will be delivered before this time? (Hint: Note that 5% of the packages will be delivered at a time beyond the guaranteed time period.) (Round your answer to one decimal place.)
hr
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Express Courier Service has found that the delivery time for packages is normally distributed, with mean 15 hours and standard deviation 2 hours.
(a) For a package selected at random, what is the probability that it will be delivered in 18 hours or less? (Round your answer to four decimal places.)
z(18) = (18-15)/2 = 3/2
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P(x <= 18) = P(z <= 3/2) = normalcdf(-100,3/2) = 0.9332
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(b) What should be the guaranteed delivery time on all packages in order to be 95% sure that the package will be delivered before this time? (Hint: Note that 5% of the packages will be delivered at a time beyond the guaranteed time period.) (Round your answer to one decimal place.)
Find the z-value with a left tail of 0.95
invNorm(0.95) = 1.645
Find the corresponding time:: t = 1.645*2+15 = 18.29 hrs = 18 hr 17 min 24 sec
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Cheers,
Stan H.
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