The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg and a standa

Question

Radda [10]

3 years ago

7

The caffeine content of a cup of home-brewed coffee is a normally distributed random variable with a mean of 115 mg and a standa

rd deviation of 20 mg. What is the 50th percentile value of caffeine content in a cup of home-brewed coffee

Mathematics

1 answer:

sdas [7] · Answer 1 · 2022-02-08T07:00:40+03:00

Answer:

115 mg

Step-by-step 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:

$z = \frac{X-mean}{SD}$

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.