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Watson Pollard
08/04/2024 · Senior High School

An elevator has a placard stating that the maximum capacity is \( 4300 \mathrm{lb}-28 \) passengers. So, 28 adult male passengers can have a mean weight of up to \( 4300 / 28=154 \) pounds. Assume that weights of males are normally distributed with a mean of 183 lb and a standard deviation of 38 lb . a. Find the probability that 1 randomly selected adult male has a weight greater than 154 lb . b. Find the probability that a sample of 28 randomly selected adult males has a mean weight greater than 154 lb . c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 154 lb is 0.7764 . (Round to four decimal places as needed.) b. The probability that a sample of 28 randomly selected adult males has a mean weight greater than 154 lb is 1.0000. (Round to four decimal places as needed.) c. Does this elevator appear to be safe? A. No, because there is a good chance that 28 randomly selected adult male passengers will exceed the B. No, because 28 randomly selected people will never be under the weight limit. C. Yes, because 28 randomly selected adult male passengers will always be under the weight limit. D. Yes, because there is a good chance that 28 randomly selected people will not exceed the elevator capacity.

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a. The probability that 1 randomly selected adult male has a weight greater than 154 lb is 0.7764. b. The probability that a sample of 28 randomly selected adult males has a mean weight greater than 154 lb is 1.0000. c. The elevator is not safe for 28 adult males because there is a high chance their combined weight will exceed the limit.

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