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

This can be solved by using the normal distribution to approximate the discrete distribution of the measurements.
It is necessary to make a correction for continuity of 0.5, therefore the z-score must be found for 60 + 0.5 = 60.5.
\[z=\frac{X-\mu}{\sigma}=\frac{60.5-50}{10}\]
When the cumulative probability for the value of z is found it must be subtracted from 1 to find the required probability.