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

$550

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=(X- 4,000)/(\sigma)`

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

`-2.12=(2,834- 4,000)/(\sigma)\\\sigma = 550`

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