Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 197 lb and a standard deviation of 40 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 nothing 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 nothing. ​(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 nothing. ​(Round to four decimal places as​ needed.) d. Is the new capacity of 20 passengers​ safe?Since the probability of overloading is

▼

over 50 % commaover 50%,

under 5 % commaunder 5%,

the new capacity

▼

does not appeardoes not appear

appearsappears

to be safe enough.

Answer 1

a)maximum mean weight is =3750/25=150

b)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	197
std deviation   =σ=	40.0000
sample size       =n=	25
std error=σx̅=σ/√n=	8.0000

probability =

P(X>150)

=

P(Z>-5.875)=

1-P(Z<-5.88)=

1-0=

1.0000

c)

probability that their mean weight exceeds 187.5 ​lb

probability =

P(X>187.5)

=

P(Z>-1.062)=

1-P(Z<-1.06)=

1-0.1446=

0.8554

Since the probability of overloading is  over 50 % the new capacity does not appears

to be safe enough.