Find the probability that 15 randomly selected passengers will have a mean weigh

Question

Find the probability that 15 randomly selected passengers will have a mean weight that is greater than 160 lb (so that their total weight is greater than the gondola maximum capacity of 2400 lb)

A ski gondola carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 15 people or 2400 lb. 2400 lb That capacity will be exceeded if 15 people have weights with a mean greater than 160 lb. Assume that weights of 15 passengers are normally distributed with a mean of 180.2 lb and a standard deviation of 41 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 160 lb. .6889 (Round to four decimal places as needed.) b. Find the probability that 15 randomly selected passengers will have a mean weight that is greater than 160 lb (so that their total weight is greater than the gondola maximum capacity of 2400 lb) (Round to four decimal places as needed.)

Explanation / Answer

Answer:

Find the probability that 15 randomly selected passengers will have a mean weight that is greater than 160 lb (so that their total weight is greater than the gondola maximum capacity of 2400 lb)

a).

z value for 160, z =(160-180.2)/41 = -0.49

p( x >160) = P(z > -0.49)

=0.6879

b).

standard error = 41/sqrt(15)   =10.5862

z value for 160, z =(160-180.2)/10.5862 = -1.91

P( mean x >160) = P( z > -1.91)

=0.9719

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