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.)
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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