I was reading some things about normal distribution and saw this problem in a text a couple days ago. I know it might be a little advanced for me at the moment, but I was wanted to know if someone can help me to see how you would solve this problem.
Assume that the lifetime in hours of a computer chip is normally distributed with mean $5000$ hours. If a producer wants at least $80%$ of the chips to have lifetimes exceeding $4200$ hours, what is the largest value the standard deviation $\sigma$ can have?
I know from reading that we can find the cutoff value of $\sigma_c$ which corresponds to exactly $80%$ having lifetimes exceeding $4200$ hours.
Here is how I did the part of the problem:
We find that $0.80*4200=3360$
$Z=X-\mu/\sigma$
$P(X\geq 4200.5)$ $=$ $4200.5-5000/\sigma$
Is it ok if someone can help me solve this type of problem? It looks like something good to know for the future.