Final answer:
To find the value of the standard deviation, we need to use the concept of the standard normal distribution and the z-score. By using the formula z = (x - mean) / standard deviation, we can calculate the standard deviation by rearranging the formula as standard deviation = (x - mean) / z.
Step-by-step explanation:
To find the value of the standard deviation of the monthly earnings of the computer systems analysts, we need to use the concept of the standard normal distribution. We know that 1.07% of the systems analysts have a monthly income of more than $6,140. This corresponds to the area under the standard normal distribution curve to the right of $6,140. Using a standard normal distribution table or a calculator, we can find the z-score that represents this area.
Once we have the z-score, we can use the formula z = (x - mean) / standard deviation to solve for the standard deviation. Rearranging the formula, we have standard deviation = (x - mean) / z. Plugging in the values of x = $6,140, mean = $4,300, and z-score from the table, we can calculate the standard deviation.