Question

Suppose $X$ has a normal distribution with mean $25$ and standard deviation of five. Between what values of $x$ do $68\%$ of the values lie

Short answer

The range of $x$value is $(20,30)$.

Step-by-step solution

Given Information

$X$ has a normal distribution with mean $25$ and standard deviation five.

Explanation

According to the empirical rule of normal distribution, it is known that within one standard deviation of the mean, there are approximately $68\%$ values of $x$ lies.

According to the provided details, the random variable $X$ follows normal

distribution with parameter $(25,5)$. Hence, the range of $x$ values can be calculated as below:

$=\mu \pm l\sigma$

$=25\pm 1\times 5$

$=25\pm 5$

$=(20,30)$

Therefore, the range of $x$ value is $(20,30)$.