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 15 people or 2505lb. That capacity will be exceeded if 15 people have weights with a mean greater than 167lb. Assume that weights of passengers are normally distributed with a mean of 179.7lb and a standard deviation of 41.2.

Find the probability that 15 randomly selected passengers will have a mean weight that is greater than 167lb? (so that their total weight is greater than the gondola maximum capacity of 2505lb) round for decimal places

Explanation / Answer

Here mean=179.7 and sd=41.2

WE need to find P(xbar>167)=P(z>167-179.7/(41.2/sqrt(15))

As per central limit theorem if population is normal sample mean will be normal with mean=mu and sd=sd/sqrt(n)

So we got P(z>-1.194)=0.8838

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