Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 193lb and a standard deviation of 41lb. The gondola has a stated capacity of 25 ​passengers, and the gondola is rated for a load limit of 3750lb. Complete parts​ (a) through​ (d) below.

a. Given that the gondola is rated for a load limit of 3750lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers?

b. if the gondola is filled with 25 random 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 random selected skiers, what is the probability that their mean weight exceeds 175 lb which is the max mean weight that does not cause the total load to exceed 3750lb.

d. is the new capacity of 20 passengers safe?

Answer 1

a_)

for normal distribution z score =(X-μ)/σx
mean μ=	193
standard deviation σ=	41

std error=σx̅=σ/√n=

8.200

maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 passengers =3750/25 =150

b) probability that their mean weight exceeds the value from part a

probability =P(X>150)=P(Z>(150-193)/8.2)=P(Z>-5.24)=1-P(Z<-5.24)=1-0=1.0000

c)

std error=σx̅=σ/√n=

9.1679

probability that their mean weight exceeds 175 lb :

probability =P(X>175)=P(Z>(175-193)/9.168)=P(Z>-1.96)=1-P(Z<-1.96)=1-0.025=0.9750

d)

since there is a high chance that their mean weight exceeds 175 lb ; the new capacity of 20 passengers is not safe .