Question

1) A ski gondola carries skiers to the top of a mountain. Assume that weights of skiers are normally distributed with a mean of 182 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 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 __ lb.

2) An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 150 lb and 201 lb. The new population of pilots has normally distributed weights with a mean of 156 lb and a standard deviation of 29.4 lb

a. If a pilot is randomly​ selected, find the probability that his weight is between 150lb and 201 lb. The probability is approximately ___ Round to the fourth decimal places if needed.

Answer 1

1] Maximum mean weight of the passenger = 3500/25 = 140 lb

2a] Since μ=156 and σ=29.4 we have:

P ( 150<X<201 )=P ( 150−156< X−μ<201−156 )=P ((150−156/29.4<(X−μ)/σ<(201−156)/29.4)

Since Z=(x−μ)σ/ , 150−15629.4=−0.2 and 201−15629.4=1.53 we have:

P ( 150<X<201 )=P ( −0.2<Z<1.53 )

Use the standard normal table to conclude that:

P ( −0.2<Z<1.53 )=0.5163