Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 201 lb and a standard deviation of 36 lb. The gondola has a stated capacity of 25 passengers, and the gondola is rated for a load limit of 3750 Ib. Complete parts (a) through (d) below a. Given that the gondola is rated for a load limit of 3750 lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers? The maximum mean weight islb (Type an integer or a decimal. Do not round.) 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)? The probability is (Round to four decimal places as needed.) 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 187.5 lb, which is the maximum mean weight that does not cause the total load to exceed 3750 lb? The probability is (Round to four decimal places as needed.) d. Is the new capacity of 20 passengers safe? Since the probablity of overioading ia he new capacty to be safe enough. the new capacity over 50%, under 5%

Answer 1

a)maximum mean weight =3750/25=150

b)

P(Xbar>150)=P(Z>(150-201)*sqrt(25)/36)=P(Z>-7.08)=1.0000

c)P(Xbar>187.5)=P(Z>(187.5-201)*sqrt(20)/36)=P(Z>-1.68)=0.9535

d)

since the probability of overloading is over 50% ; the new capacity is not to be safe enough