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The new science and math building on campus has four elevators each designed to carry a maximum 8 people. A building safety study has found that the combined weight of 8 people can be modeled by normal distribution with mean of 1400 pounds and a standard deviation of 120 pounds. 0.7887 0.1056 0.1056 1 -3 -2 F 1 -1.25 1.25 Using the figure of a standard normal distribution, is the following statement valid or not valid? We would expect the total weight of 8 people to be between 1250 and 1550 pounds more than 75% of the time.

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The total weight of 8 people to be more than 1500 pounds less than 20% of the time.

The new science and math building on campus has four elevators each designed to carry a maximum 8 people.

A building safety study has found that the combined weight of 8 people can be modeled by normal distribution with mean of 1400 pounds and a standard deviation of 120 pounds.

Given

mean = 1400

standard deviation = 120

P(X > 1500) = P((x-u)/s > (1500 - 1400)/120)

= P(z > 0.83)

= 0.2032694 [since from z table]

= 0.2033

= 20%

So we would expect the total weight of 8 people to be more than 1500 pounds less than 20% of the time.

Hence the answer is the total weight of 8 people to be more than 1500 pounds less than 20% of the time.

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