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?

Respuesta :

[tex]\mathbb P(X>60)=\mathbb P\left(\dfrac{X-50}{10}>\dfrac{60-50}{10}\right)=\mathbb P(Z>1)[/tex]

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.