11. Assume that the weights of individuals are independent and normally distributed with a mean of 160 lbs. and a standard deviation of 30 lbs. Suppose that 25 people squeeze into an elevator that is designed to hold 4300 lbs. Determine the following:

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part C D

11. Assume that the weights of individuals are independent and normally distributed with a
mean of 160 Ibs. and a standard deviation of 30 lbs. Suppose that 25 people squeeze
into an elevator that is designed to hold 4300 lbs. Determine the following:
(a) The expected value and variance of the mean weight of the people.
(b) Probability that the mean weight of the people is within 4 Ibs. of 160 lbs.
(c) The probability that the load (the total weight) exceeds the design limit.
(d) The design limit that is exceeded by 25 occupants with probability 0.0001.
Transcribed Image Text:11. Assume that the weights of individuals are independent and normally distributed with a mean of 160 Ibs. and a standard deviation of 30 lbs. Suppose that 25 people squeeze into an elevator that is designed to hold 4300 lbs. Determine the following: (a) The expected value and variance of the mean weight of the people. (b) Probability that the mean weight of the people is within 4 Ibs. of 160 lbs. (c) The probability that the load (the total weight) exceeds the design limit. (d) The design limit that is exceeded by 25 occupants with probability 0.0001.
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