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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?

Verified Answer :

LammettHash

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

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.

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