Question

# A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers...

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.

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

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.

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