Elementary statistics

Question

a ski gondola carries skiers Bro the top of a mountain. assume that weights are normally distributed with a mean of 200 lb and a standard deviation of 39 lb. the gondola has a stated capacity of 25 passengers and the gondola is rated for a load limit of 3750 lb. if the gondola is filled with 25 randomly selected skiers what is the probability that their mean weight exceeds the value from part a

Answer 1

Question: A ski gondola carries skiers to the top of a mountain. assume that weights are normally distributed with a mean of 200 lb and a standard deviation of 39 lb. The gondola has a stated capacity of 25 passengers and the gondola is rated for a load limit of 3750 lb. If the gondola is filled with 25 randomly selected skiers what is the probability that their mean weight exceeds the value from part a

Answer: Firstly, as "the value from a" is not clear, I will take a hint from similar problems and assume that "the value from a" refers to the average weight of one person when the gondola is at capacity. Capacity is 25 passengers, and the gondola has a load limit of 3,750 pounds. I'll say this value is 3,750/25 = 150 pounds.

Even though our sample is small for statistical purposes, we can use the normal distribution since the weights of skiers are known to be a normally distributed phenomenon.

Let's set up a z-score:

z = [(150) - (200)] / (39 / sqrt(25))

z = -50 / (39/5)

z ≈ -6.4103

We are looking for the probability that our 25 skiers will exceed capacity; that is, P(z > -6.4103). Perform a calculation to the effect of 1 - normalcdf(-1E99, -6.4103, 0, 1) (if the scores were standardized, else do 1 - normalcdf(-1E99, 150, 200, 39/sqrt(25)). The probability comes to about .9999.

The probability that the skiers' mean weight exceeds the value from part a is 0.9999.