Question

Suppose$X~N(–3,1).$Between what $x$values does $95.45\%$of the data lie? The range of $x$values is centered at the mean of the distribution(i.e., –3).

Short answer

The$95.45\%$of data lies between$(-5,-1)$

Step-by-step solution

Given Information

Given in the question that, $X~N(–3,1).$

We have to find between what $x$values does $95.45\%$of the data lie?

Explanation 

According to the empirical rule of normal distribution, approximately $95\%$values $x$lies within two standard deviation of the mean.

Therefore, $95.45\%$of data also will lie approximately near to within two standard deviation of the mean.

From the information given in the question, the random variable $x$follows normal distribution with parameter $(-3,1)$

Hence, the range of $x$values can be compute as follow:

$=\mu \pm 2\sigma$

$=-3\pm 2\times 1$

$=-3\pm 2$

$=(-5,-1)$