Question

About what percent of$x$ values lie between the mean and three standard deviations?

Short answer

The $x$values which lie between the mean and three standard deviations will be:

$\approx 50\%$

Step-by-step solution

Given information

Given in the question that, We have to find percent of x values lie between the mean and three standard deviations.

Explanation

According to the empirical rule of normal distribution, within three standard deviations of the mean, there are approximately $99.7\%$values of $x$lies, therefore the percent of $x$values lie between the mean and three standard deviations will be the half of those $x$values which lie within three standard deviations of the mean because the $x$values which lie between the mean and three standard deviations will be on one side of the normal graph. Hence, the $x$values which lie between the mean and three standard deviations will be:

$=\frac{99.7\mathrm{\%}}{2}$

$\approx 50\mathrm{\%}$