Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 184lb and a standard deviation of 42lb. The gondola has a stated capacity of 25 ​passengers, and the gondola is rated for a load limit of 3500 lb. Complete parts​ (a) through​ (d) below.

a) Given that the gondola is rated for a load limit of 3500​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

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

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 175​lb, which is the maximum mean weight that does not cause the total load to exceed 3500​lb? The probability is

d) Circle the right choices

Since the probability of overloading is over 50%/or under 5% the new capacity does/does not appear safe enough

Answer 1

Solution:

a) Given that the gondola is rated for a load limit of 3500​lb, what is the maximum mean weight of the passengers if the gondola is filled to the stated capacity of 25 ​passengers?

Answer: The maximum mean weight is:

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)?

Answer: We have to find

Using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability is 0.8531

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 175​lb, which is the maximum mean weight that does not cause the total load to exceed 3500​lb?

Answer: We have to find

Using the z-score formula, we have:

Now using the standard normal table, we have:

Therefore, the probability is 0.5832

d) Circle the right choices

Since the probability of overloading is over 50% the new capacity does not appear safe enough