what level of age falls in the 87th percentile?

Question

Professor wise wanted to examine age distribution in the US. she takes a random sample of residents and collects data on age measured in years. she discovered that age is normally distributed with a mean of 48 and a standard deviation of 18.

Answer 1

If you picture the normal distribution curve (bell curve), the 87th percentile is where (starting from the very left side and moving right) 87% of the area under the curve is filled in. We can find the value of the normal distribution at that point by using a reference table and looking up 0.87, or using the invNorm function on a standard graphing calculator.

This will give the standardized value (z-score) which corresponds to the 87th percentile. From here, you can use the simple formula for the z-score to get your answer.

z = (x – μ) / σ

where μ is the mean, x is the actual value (in this case, age) and σ is the standard deviation. You figured out the z-score in the previous step, you're given μ and σ, and are solving for x.