Question

A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 186 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 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?

Answer 1

Mean weight of skier = 186 pounds

Standard deviation = 40 pounds

a) As gondola is rated for 3500 pounds for a capacity of 25 passengers.

So, maximum mean weight of the passengers

= load limit / number of passengers

= 3500 / 25

= 140 pounds ( this final answer)

b) z score = (sample mean - population mean) / std. Deviation

= (140 - 186 )/ 40

= - 46 / 40

= - 1.15

We need to find P(z > -1.15) = 1 - P(z < -1.15)

Now, look at a standard normal table to find

P(z < -1.15) = 0.12507
therefore:
P(z > -1.15) = 1 - 0.12507 = 0.87493 = 0.875

Hence, the probability that the mean weight of 25 randomly selected skiers exceeds 140 lb is about 87.5%. Which is quite high hence it's not safe.