Question

You invite into your home a random individual from a small town. Unfortunately, it's a zombie town and only a few are still normal (including you). You also know that turning into a zombie depends on the degree of exposure to a radioactive substance. The distribution of exposure is normally distributed with a mean of 2700 on radioactive measures, and a SD of 300. A person will turn into a zombie if the radioactivity exposure is at or beyond 2200. What is the probability that the person you just invited might be a zombie -- remember, zombies will eat your brain.

Answer 1

$\mu=2700, \sigma=300$

$P(X\ge2200)$ can be calculated directly using =1-NORM.DIST(2200,2700,300,TRUE) excel formula which yields 0.95221.

Similarly, $Z-score=\frac{X-\mu}{\sigma}=\frac{2200-2700}{300}=-1.667$

$P(X\ge2200)=1-P(Z<-1.667)$

From Z tables or =NORM.S.DIST(-1.66667,TRUE), $P(Z<-1.66667)=0.04779$

Thus, $P(X\ge2200)=1-0.04779=0.95221$

The probability that the invited person might be a zombie is 0.95221.