# Z-Scores and Standard Deviation

Using the sample data collected (see attached), consider the variables (satisfaction with job and satisfaction with the economy) and perform the following:

Determine what scores correspond to the top and bottom 10% and 25% of the data.

Begin with the z-score formula and transform the formula so that you are solving for the individual score (denoted as X in the z-score formula).

Determine the z-score that corresponds to the top 10% and then substitute in your values for the mean and the standard deviation. Repeat the steps for the bottom 10% and then the top and bottom 25%.

Determine what percentage will be between 3 and 7 for both variables (these scores correspond to ratings of somewhat satisfied to somewhat dissatisfied and exclude the extreme ratings of extremely satisfied and extremely dissatisfied).

Start with the z-score formula and calculate the z-score for each value. Explain the process for converting a z-score to a percentile.

Determine what scores correspond to the top and bottom 10% and 25% of the data.

Transform the z-score formula for solving for the individual score.

Determine the z-score that corresponds to the top 10% and substituted in your values for the mean and the standard deviation. Repeat the steps for the bottom 10% and the top and bottom 25%.

Determine what percentage will be between 3 and 7 for both variables.

Compute the z-score for each value. Explained the process for converting a z-score to a percentile.

#### Solution Summary

This solution is comprised of a detailed explanation of standard normal distribution or z score by hand calculation. In this solution, step-by-step explanation of this complicated topic provides students with a clear perspective of standard normal distribution to find the Z-scores using hand calculation.