Question

Assume the amount of caffeine extracted from 8 fluid ounces of coffee brewed in a drip machine is normally distributed. On average, 100 mg of caffeine is extracted with a standard deviation of 10 mg. What is the probability of extracting more than 120 mg of caffeine from 8 fluid ounces of coffee brewed in a drip machine

Answer 1

2.3%

Explanation:

Imagine a standard normal curve with mean at 100 mg. One standard deviation above the mean would be 110 mg; two standard deviations 120 mg.

Draw a vertical line through x = 120. To answer this question, we must find the area under the curve to the left of x = 120 and then subtract this result from 1.00:

Using a calculator with probability distribution functions built in, we find the area to the left of x = 120 as follows:

normcdf(-100,120,100,10) = 0.977 => 1.000 - 0.977 = 0.023

The probability of extracting more than 120 mg of caffeine from 8 fluid ounces of coffee brewed in a drip machine is 2.3%