A ski gondola carries skiers to the top of a mountain. It bears a plaque stating

Question

A ski gondola carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 16 people or 2624 lb. That capacity will be exceeded if 16 people have weights with a mean greater than 2624 lb/16 = 164 lb. Assume that weights of passengers are normally distributed with a mean of 182 lb and a standard deviation of 43.2 lb. Complete parts a through c below. a. Find the probability that it an individual passenger is randomly selected, their weight win be greater than 164 lb. b. Find the probability that 16 randomly selected passengers will have a mean weight that is greater than 164 lb (so that their total weight is greater than the gondola maximum capacity of 2624 lb) c. Does the gondola appear to nave the correct weight limit? Why or why not? A. Yes the odds that every passenger will have a weight greater than 164 lb is very low so the total weight will likely be under the maximum capacity. B. Yes only about half or the passengers will have a weight greater than 164 lb, so the total weight will likely be under the maximum capacity. c. Does the gondola appear to have the correct weight limit? Why or why not? A. Yes, the odds that every passenger will have a weight greater than 164 lb is very low, so the total weight will likely be under the maximum capacity. B. Yes, only about half of the passengers will have a weight greater than 164 lb, so the total weight will likely be under the maximum capacity. C. No, there is a good chance that any individual passenger has a weight greater than 164 lb, so the gondola needs to be able to support more weight. D. No, there is a high probability that the gondola will be overloaded if it is occupied by 16 passengers, so it appears that the number of allowed passengers should be reduced.

Explanation / Answer

a)P(X>164)=P(Z>(164-182)/43.2)=P(Z>-0.4167)=0.6615

b)here std error of mean =std deviation/(n)1/2 =43.2/(16)1/2 =10.8

therefore P(X>164)=P(Z>(164-182)/10.8)=P(Z>-1.6667)=0.9522

c) option D is correct.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.