31. Mortgage Industry Employees. In an issue of National Mortgage News, a special report was published on publicly traded mortgage industry companies. A sample of $25$mortgage industry companies had the following numbers of employees.

a. Obtain a normal probability plot of the data.
b. Use part (a) to identify any outliers.
c. Use part (a) to assess the normality of the variable under consideration.

A sample of $25$mortgage industry companies had the following numbers of employees.

The random variable $X$'s $z-$ score is calculated as follows:
$z=\frac{x-\mu }{\sigma }$where, $\mu$indicates the mean and $\sigma$ indicates the standard deviation.
The mean is $\mu =6965.12$
The variance is $\sigma =8415.98759$
The $z-$scores for the given values are listed in the table below:

The number of employees is plotted on the horizontal axis, while the normal scores are plotted on the vertical axis.

To identify the outliers by using part (a).

An outlier is a data point that deviates from the plot's overall pattern.
There isn't a single observation that deviates from the plot's overall pattern.
As a result, there are no outliers.

To assess the normality of the variable under consideration by using part (a).

The values of the sample are normally distributed if the normal probability plot is generally linear.
The plot does not follow a linear pattern.
As a result, the observations will fail to satisfy the normal requirement.