Question

A distribution of measurements is relatively mound-shaped

with mean 50 and standard deviation 10.
If a measurement is chosen at random from this distribution, what is the probability that it will be greater than 60?

Answer 1

`\mathbb P(X>60)=\mathbb P\left((X-50)/(10)>(60-50)/(10)\right)=\mathbb P(Z>1)`

Since approximately 68% of a (roughly) normal distribution falls within one standard deviation of the mean, that leaves 32% that falls outside, and by symmetry 16% should lie above one standard deviation of the mean.