1. ## Normal Distribution

Suppose that in an apartment building run by the Probandstat rental company, the
inhabitants's weights follow a normal distribution with mean 73.0 kilos and standard
deviation 13.65 kilos. A new elevator must be installed. The elevator company rates the safe carrying capacity of the new elevator to be 895 kilos, but publishes the rated
capacity as only 730 kilos. A manager at the apartment (must have been a new hire)
reasoned as follows, “Since the average resident weighs 73 kilos and the elevator safely carries 730 kilos, the safe capacity for the elevator in our building must be 10
passengers.”

a) Show that this is incorrect by showing that the probability that ten randomly selected inhabitants would have a total weight exceeding the supposed rated weight capacity of 730 is one-half.

b) However, now find the probability that ten randomly selected inhabitants would have a total weight exceeding the actual carrying capacity of 895.

Good thing the elevator company built in a margin of error!

2. ## Re: Normal Distribution

Well...what do you think about how to solve it? Maybe this could be the starting point

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