Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of

194

lb and a standard deviation of

37

lb. The gondola has a stated capacity of

25

​passengers, and the gondola is rated for a load limit of

3750

lb. 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 is

150

lb.

​(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.)

Answer 1

a)

maximum mean weight of the passengers if the gondola is filled to the stated capacity of25 ​passengers

=3750/25 =150

b)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	194
std deviation   =σ=	37.000
sample size       =n=	25
std error=σx̅=σ/√n=	7.40

probability =P(X>150)=P(Z>(150-194)/7.4)=P(Z>-5.95)=1-P(Z<-5.95)=1-0=1.0000

c)

sample size       =n=	20
std error=σx̅=σ/√n=	8.2735

probability =P(X>187.5)=P(Z>(187.5-194)/8.273)=P(Z>-0.79)=1-P(Z<-0.79)=1-0.2148=0.7852