Question

About what percent of $x$ values lie between the first and third standard deviations(both sides)?

Short answer

About $32\%$ of the $x$ values from normal distribution will lie between first and third standard deviation.

Step-by-step solution

Given information

Given in the question that, We have to find the percent of $x$values lie between the first and third standard deviations(both sides).

Explanation

According to the empirical rule of normal distribution, within one standard deviation of the mean, there are approximately $68\%$values of $x$lies and within three standard deviations of the mean, there are approximately $99.7\%$values of $x$lies. So, the percent of the $x$values from normal distribution lie between first and third standard deviation from the mean will be:

$=99.7\mathrm{\%}-68\mathrm{\%}$

$=31.7\mathrm{\%}$

$\approx 32\mathrm{\%}$