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Gondola Safety A ski gondola in Vail, Colorado, carries
Chapter 6, Problem 17BSC(choose chapter or problem)
Gondola Safety A ski gondola in Vail, Colorado, carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 12 people or 2004 lb. That capacity will be exceeded if 12 people have weights with a mean greater than 2004 / 12 = 167 lb . Because men tend to weigh more than women, a worst-case scenario involves 12 passengers who are all men. Assume that weights of men are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb (based on Data Set 1 in Appendix B).
a. Find the probability that if an individual man is randomly selected, his weight will be greater than 167 lb.
b. Find the probability that 12 randomly selected men will have a mean weight that is greater than 167 lb (so that their total weight is greater than the gondola maximum capacity of 2004 lb).
c. Does the gondola appear to have the correct weight limit? Why or why not?
Questions & Answers
QUESTION:
Gondola Safety A ski gondola in Vail, Colorado, carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 12 people or 2004 lb. That capacity will be exceeded if 12 people have weights with a mean greater than 2004 / 12 = 167 lb . Because men tend to weigh more than women, a worst-case scenario involves 12 passengers who are all men. Assume that weights of men are normally distributed with a mean of 182.9 lb and a standard deviation of 40.8 lb (based on Data Set 1 in Appendix B).
a. Find the probability that if an individual man is randomly selected, his weight will be greater than 167 lb.
b. Find the probability that 12 randomly selected men will have a mean weight that is greater than 167 lb (so that their total weight is greater than the gondola maximum capacity of 2004 lb).
c. Does the gondola appear to have the correct weight limit? Why or why not?
ANSWER:Answer :
Step 1 of 3 :
Given, A ski gondola in Vail, Colorado, carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 12 people or 2004 lb. That capacity will be exceeded if 12 people have weights with a mean greater than 2004/12 = 167 lb. Because men tend to weigh more than women, a worst-case scenario involves 12 passengers who are all men.
We have to assume that weights of men are normally distributed with mean of 182.9 lb and a standard deviation of 40.8 lb
- We have to find the probability that if an individual man is randomly selected, his weight will be greater than 167 lb.
z-score is the value decrease by the mean, divided by the standard deviation.
Z =
Where , = 167
Z =
= -0.39
Then, P(z > -0.39)
= 1 - P(z < -0.39)
= 1 - 0.3483 (from area under normal curve table)
= 0.6517
0.6517 the probability that if an individual man is randomly selected, his weight will be greater than 167 lb.