Question

The monthly earnings of computer programmers are normally distributed with a mean of $4,000. If only 1.7 percent of programmers have monthly incomes of less than $2,834, what is the value of the standard deviation of the monthly earnings of the computer programmers?

Answer 1

Answer:

$550

Step-by-step explanation:

The 1.7th percentile of a normal distribution has a corresponding z-score of -2.12

For any given  value of monthly earnings, X, the z-score is defined as:

$z=\frac{X- 4,000}{\sigma}$

For z=-2.12, and X = 2,834, the standard deviation is:

$-2.12=\frac{2,834- 4,000}{\sigma}\\\sigma = 550$

The standard deviation of the monthly earnings of the computer programmers is $550.