The citizens of Burgton have normally distributed body weights with a mean of 16

Question

The citizens of Burgton have normally distributed body weights with a mean of 168 pounds. And a standard deviation of 20 pounds. If an elevator in town has a maximum capacity of 25 persons and a rated maximum weight of 4500 pounds, what is the probability that the elevator, when filled to capacity, will not exceed its rated weight? (In other words what is the probability that a sample of 25 citizens will have a mean weight of less than 180 pounds?) The citizens of Burgton have normally distributed body weights with a mean of 168 pounds. And a standard deviation of 20 pounds. If an elevator in town has a maximum capacity of 25 persons and a rated maximum weight of 4500 pounds, what is the probability that the elevator, when filled to capacity, will not exceed its rated weight? (In other words what is the probability that a sample of 25 citizens will have a mean weight of less than 180 pounds?)

Explanation / Answer

here std error of mean =std deviation/(n)1/2 =20/(25)1/2 =4

therefore probability that a sample of 25 citizens will have a mean weight of less than 180 pounds

=P(X<180) =P(Z<(180-168)/4) =1-P(Z<3) =1-0.9987 =0.0013

pelase reply for any clarification

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