Sampling Distribution - Tricky problem that I'm sure is actually quite easy

StarchyTubers

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Aug 4, 2018
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Hey Gang,

So I feel like I've gotten the hang of sampling distribution so far, but I've encountered a question thats really throwing my brain through a loop trying to find the answer to and my online class doesn't really cover how to approach these questions :( Anyways, heres the question:

An elevator company has conducted a study and determined the average adult weight is 65 kg with a standard deviation of 15 kg. The distribution is approximately normally distributed.

a. The company has decided that the elevator will have a capacity of 5 people and a maximum load of 475 kg. What is the probability that load will be exceeded if there are 5 people in the elevator?

So, looking at the solution, I know the answer is a Z score of 4.47, and I've tried to reverse engineer this the best I could, but I still cant figure it out! Any help is appreciated!

 
I actually did figure it out, well, figured out enough to get the desired answer ahaha. I scaled the std dev for a sample size of 5, also divided the 475 by five. My Z test was (95-65)/6.7082..., which gave me the correct answer!
 
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