Question

the capacity of an elevator is 15 people of 2625 pounds. the capacity will be exceeded if 15 people have weights with a mean greater than 2625/15=175 pounds. suppose the people have weights that are normally distributed with a mean of 180 lb and a standard deviation of 31 lb
find the probability that a person is randomly selected, his weight will be greater than 175 pounds.

find the probability that 15 randomly selected people will have a mean that is greater than 175 pounds.

Answer 1

Given that, mean (μ) = 180 lb and standard deviation $(\sigma)$ = 31 lb

sample size (n) = 15

We want to find,

P(X > 175)

P(X > 175) X-4 175 – 180 = PIE = P(Z > -0.62) = P(Z < 0.62) = 0.7324

Therefore, required probability is 0.7324