Question

The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg and a standard deviation of 20 mg. What is the 50th percentile value of caffeine content in a cup of home-brewed coffee

Answer 1

115 mg

Explanation:

The 50th percentile has a corresponding z-score of z = 0. The z-score, for any given value of caffeine, X, is given by:

`z = (X-mean)/(SD)`

Therefore, if z=0, then X must be equal to the mean value of the normal distribution, which is 115 mg. Thus, the 50th percentile value of caffeine content is 115 mg.