Problem

A normal distribution has a mean of 12 and a standard deviation of 3. Use the 68-95-99.7 rule to find the percentage of values in the distribution above 18.

Solution

Step 1 :A normal distribution has a mean of 12 and a standard deviation of 3. We are asked to find the percentage of values in the distribution above 18.

Step 2 :The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

Step 3 :In this case, the mean is 12 and the standard deviation is 3. So, one standard deviation above the mean is 15 (12+3), two standard deviations above the mean is 18 (12+3+3).

Step 4 :Therefore, the percentage of values above 18 is the percentage of values that fall beyond two standard deviations from the mean. According to the empirical rule, 95% of the data falls within two standard deviations of the mean. This means that 5% of the data falls outside of two standard deviations from the mean. Since the normal distribution is symmetric, this 5% is split evenly between the two tails of the distribution.

Step 5 :So, the percentage of values in the distribution above 18 is 2.5%.

Step 6 :Final Answer: The percentage of values in the distribution above 18 is \(\boxed{2.5\%}\).

From Solvely APP
Source: https://solvelyapp.com/problems/17849/

Get free Solvely APP to solve your own problems!

solvely Solvely
Download