Question

The City of Decatur finds that salaries for residents working in the technology sector follow an approximately normal distribution with a mean of $42,800 and a standard deviation of $8,365.

To the nearest hundredth, what Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000?

Answer 1

- 1. 15

Explanation:

Z score is used in statistic to calculate deviation of an observed value from mean value of sample of observation.

Mathematically it is given by

`z = observed \ value - mean\ value/ standard\ deviation`

using the above formula and substituting the value of of

mean = $42,800

standard deviation = $8,365

observed value =$30,000

Z = (8,365 - 42,800) / $30,000

= - 34,435/ 30,000 = - 1. 14783

= - 1. 15 ( to the nearest hundredth)

- 1. 15 Z-Score would be used to determine the percentage of residents working in the technology sector who earn more than $30,000