Page 11 of 12 28. A ski gondola carries skiers to the top of a mountain. t bears
ID: 3334321 • Letter: P
Question
Page 11 of 12 28. A ski gondola carries skiers to the top of a mountain. t bears a plaque stating that the maximum capacity is 14 people 2366 lb 14 2366 lb. That capacity will be exceeded if 14 people have weights with a mean greater than : 169 lb. Assume that weights of passengers are normally distributed with a mean of 183.6 lb and a standard deviation of 40.2 lb. Complete parts a through c below a. Find the probability that if an individual passenger is randomly selected, their weight will be greater than 169 Ib. (Round to four decimal places as needed.) b. Find the probability that 14 randomly selected passengers will have a mean weight that is greater than 169 lb (so that their total weight is greater than the gondola maximum capacity of 2366 lb) (Round to four decimal places as needed.) c. Does the gondola appear to have the correct weight limit? Why or why not? O A. Yes, only about half of the passengers will have a weight greater than 169 lb, so the total weight O B. No, there is a good chance that any individual passenger has a weight greater than 169 lb, so O C. Yes, the odds that every passenger will have a weight greater than 169 lb is very low, so the 0 D. No, there is a high probability that the gondola will be overloaded if it is occupied by 14 will likely be under the maximum capacity the gondola needs to be able to support more weight total weight will likely be under the maximum capacity. passengers, so it appears that the number of allowed passengers should be reduced.Explanation / Answer
A) P(X > 169) = P((X - mean)/sd > (169 - mean) /SD)
= P(Z > (169 - 183.6)/40.2)
= 1 - P(Z < -0.36)
= 1 - 0.3594 = 0.6406
B) P(x > 169) = P((x - mean) /(SD/sqrt(n)) > (169 - mean)/(SD/sqrt(n))
= P(Z > (169 - 183.6)/(40.2/sqrt(14))
= 1 - P(Z < -1.36)
= 1 - 0.0869 = 0.9131
C) Option-C is the correct answer.
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