The longevity of people living in certain locality has a standard deviation of 14 years. What is the mean longevity if 30% of the people live longer than 75 years? Assume a normal distribution for life spans.

The longevity of people living in certain locality has a standard deviation of 14 years. What is the mean longevity if 30% of the people live longer than 75 years? Assume a normal distribution for life spans.


If 30% live longer than 75 years, then 70% live 75 years or less.

Since the normal distribution moves left to right, we want the area in the upper 30% shaded. Look up the z-score for .7

Then, use z=\frac{75-{\mu}}{14}

and solve for {\mu}