Answer to Question #155910 in Statistics and Probability for bert

Question

Given a normal distribution with a standard deviation of 14, what is the mean if 40% of the values are below 60?

Answer 1

We have that

$\sigma = 14$

$P(X<60)=0.4$

$P(X<60)=P(Z<\frac{60 - \mu}{\sigma})=0.4$

Z-value of –0.25 corresponds to 40% of the area under the curve.

Then

$\frac{60-\mu}{\sigma}=-0.25 \implies \mu=60+0.25\cdot\sigma=60+0.25\cdot14=63.5$

Answer: the mean is 63.5