According to a recent Gallup Poll, American men, on average, say they weigh 196 lbs women say they weigh 160 lbs (source Gallup com) The sign in the main elevator in the new River Park Municipal Building identifies the maximum capacity of the elevator as 10 people, based on an average passenger weight of 200 lbs a If weights for men have a normal distribution with a mean of 196 lbs and a standard deviation, m, of 30 lbs , how likely is it that 10 random men getting on the elevator will have a total weight greater than 2000 lbs Greater than 2250 lbs b If weights for women have a normal distribution with a mean of 160 lbs and a standard deviation, w, of 20 lbs , how likely is it that 10 random women getting into the elevator will have a total weight greater 2000 lbs Greater than 1700 lbs

Question: According to a recent Gallup Poll, American men, on average, say they weigh 196 lbs.; women say they weigh 160 lbs. (source: Gallup.com). The sign

According to a recent Gallup Poll, American men, on average, say they weigh 196 lbs.; women say they weigh 160 lbs. (source: Gallup.com). The sign in the main elevator in the new River Park Municipal Building identifies the maximum capacity of the elevator as 10 people, based on an average passenger weight of 200 lbs.
a. If weights for men have a normal with a mean of 196 lbs. and a standard deviation, σm, of 30 lbs., how likely is it that 10 random men getting on the elevator will have a total weight greater than 2000 lbs.? Greater than 2250 lbs.?
b. If weights for women have a normal with a mean of 160 lbs. and a standard deviation, σw, of 20 lbs., how likely is it that 10 random women getting into the elevator will have a total weight greater 2000 lbs.? Greater than 1700 lbs.?

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