Question

A normal distribution has a mean of 13.9 and a standard deviation of 2.6. What percent of the data will be less than 8.7?

Answer 1

Step-by-step explanation

To solve this question, we can use the empirical rule

The empirical rule, also referred to as the three-sigma rule or 68-95-99.7 rule, is a statistical rule which states that for a normal distribution.

So if the mean is 13.9 and the standard deviation is 2.6

Then to obtain 8.7, there must have been 2 standard deviations below the mean. That is:

`13.9-2(2.6)=8.7`

From the above, we can see that the per cent that will be less than 2 standard deviations below the mean is approximately

`0.1\text{ \% +2.4 \% =2.5 \%}`

Thus, about 2.5% will be less than 8.7