Question

8 Suppose the average high school teachers annual salary is $53,000. Assume teacher salary is normally distributed with a standard deviation of $19,000. What percent of high school teachers make between $51,000 and $55,000

Answer 1

Solution:

Given that,

mean = = 53,000

standard deviation = = 19,000

p ( 51,000 < x < 55,000)

= p ( 51,000 - 53,000 / 19,000) < ( x -  / ) < ( 55,000 - 53,000 / 19,000)

= p ( - 2,000 / 19,000 < z < 2,000 / 19,000 )

= p (- 0.11 < z < 0.11 )

= p (z < 0.11 ) - p ( z < - 0.11 )

Using z table

= 0.5438 - 0.4562

= 0.0876

Probability = 08.76%