An online shopping company promises that fresh food order will be delivered to a housechold within 90 minutes. The marketing manager of the company reviews the delivery time of all orders in the last month and finds that the delivery time follows a normal distribution with mean delivery time of 77.5 minutes and standard deviation of 10.5 minutes. (a) Find the probability that an order can be delivered to the customer before the promise time. (b) The marketing manager wants to adjust the promise time from 90 minutes to a new level: K minutes, so that only 0.3% of the orders would arrive after K minutes. What should the value of K be? (Round off your answer to the nearest minute.) (c) If the delivery time of each order will be reduced by 2.5%. Find the new mean and new standard deviation of the delivery time after the change.
An online shopping company promises that fresh food order will be delivered to a housechold within 90 minutes. The marketing manager of the company reviews the delivery time of all orders in the last month and finds that the delivery time follows a normal distribution with mean delivery time of 77.5 minutes and standard deviation of 10.5 minutes. (a) Find the probability that an order can be delivered to the customer before the promise time. (b) The marketing manager wants to adjust the promise time from 90 minutes to a new level: K minutes, so that only 0.3% of the orders would arrive after K minutes. What should the value of K be? (Round off your answer to the nearest minute.) (c) If the delivery time of each order will be reduced by 2.5%. Find the new mean and new standard deviation of the delivery time after the change.
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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Transcribed Image Text:An online shopping company promises that fresh food order will be delivered to a household within 90 minutes.
The marketing manager of the company reviews the delivery time of all orders in the last month and finds that
the delivery time follows a normal distribution with mean delivery time of 77.5 minutes and standard deviation
of 10.5 minutes.
(a) Find the probability that an order can be delivered to the customer before the promise time.
(b) The marketing manager wants to adjust the promise time from 90 minutes to a new level: K minutes, so
that only 0.3% of the orders would arrive after K minutes. What should the value of K be? (Round off
your answer to the nearest minute.)
(c) If the delivery time of each order will be reduced by 2.5%. Find the new mean and new standard
deviation of the delivery time after the change.
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