An employer pays a mean salary for a 5 -day workweek of ...

An employer pays a mean salary for a 5 -day workweek of $\$ 1250$ with a standard deviation of $\$ 129$ On the weekends, his salary expenses have a mean of \$450 with a standard deviation of $\$ 57 .$ What is the mean and standard deviation of his total weekly salaries?

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Key Concepts

Standard Deviation and Variance

Standard deviation measures the dispersion or spread of a set of values around the mean, while variance is the square of the standard deviation. For independent random variables, the overall variance is the sum of the individual variances, and the standard deviation is the square root of this total variance, quantifying the overall risk or uncertainty in the total salary.

Mean

The mean is the measure of central tendency that provides the expected value of a random variable. In the context of summing salaries, the overall mean is computed by adding the mean salary of the workweek and the mean salary of the weekend, representing the employer's expected total weekly salary.

Sum of Independent Random Variables

When dealing with independent random variables, the total value obtained by summing them has a mean equal to the sum of their individual means and a variance equal to the sum of their individual variances. This principle is widely used in statistics to combine different sources of variability into a single overall measure.

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