a ski gondola carries skiers to the top if a mountain. assume the weights of ski

Question

a ski gondola carries skiers to the top if a mountain. assume the weights of skiers are normally distributed with a mean of 180 lb and a standard deviation of 38 lb. the gondola has a stated compacity of 25 passengers, and the gondola is rated fir a load limit of 3500 lb A. Given that the gondola is rated for a load limit of 3500 lb what is the max mean weight of the passengers if the gondola is filled to the capacity of 25 passengers? B. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part A. C. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the max weight hat does not cause the total load to exceed 3500lb D. Is the new capacity of 20 passengers safe? Since the probability of overloading is (under 5%, over 50%) the new capacity (does not appear, appears) to be safe enough. a ski gondola carries skiers to the top if a mountain. assume the weights of skiers are normally distributed with a mean of 180 lb and a standard deviation of 38 lb. the gondola has a stated compacity of 25 passengers, and the gondola is rated fir a load limit of 3500 lb A. Given that the gondola is rated for a load limit of 3500 lb what is the max mean weight of the passengers if the gondola is filled to the capacity of 25 passengers? B. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part A. C. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the max weight hat does not cause the total load to exceed 3500lb D. Is the new capacity of 20 passengers safe? Since the probability of overloading is (under 5%, over 50%) the new capacity (does not appear, appears) to be safe enough. A. Given that the gondola is rated for a load limit of 3500 lb what is the max mean weight of the passengers if the gondola is filled to the capacity of 25 passengers? B. If the gondola is filled with 25 randomly selected skiers, what is the probability that their mean weight exceeds the value from part A. C. If the weight assumptions were revised so that the new capacity became 20 passengers and the gondola is filled with 20 randomly selected skiers, what is the probability that their mean weight exceeds 175 lb, which is the max weight hat does not cause the total load to exceed 3500lb D. Is the new capacity of 20 passengers safe? Since the probability of overloading is (under 5%, over 50%) the new capacity (does not appear, appears) to be safe enough.

Explanation / Answer

a) max mean weight of the passengers =3500/25=140

b)

probability that their mean weight exceeds 140 lb:

c)

d)Since the probability of overloading is  over 50% the new capacity  does not appear to be safe enough.

for normal distribution z score =(X-)/ here mean=       = 180 std deviation   == 38.000 sample size       =n= 25 std error=x=/n= 7.6000

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