Question

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

8. A ski gondola carries skiers to the top of a mountain. It bears a plaque stating that the maximum capacity is 13 people or 2132 lb. That capacity will be exceeded if 13 people have weights with a mean greater than 2132lb/13 = 164 lb. Assume that weights of passengers are normally distributed with a mean of 181 lb and a standard deviation of 40.9 lb. Complete parts a through c below.

Find the probability that 13 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 2132 ​lb)

​(Round to four decimal places as​ needed.)

12. An airliner carries 250 passengers and has doors with a height of 72 in. Heights of men are normally distributed with a mean of 69.0 in and a standard deviation of 2.8 in. Complete parts​ (a) through​ (d).

If half of the 250 passengers are​ men, find the probability that the mean height of the 125 men is less than 72 in.

The probability is____.

​(Round to four decimal places as​ needed.)

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