Normal Percentile

Question

the average beginning annual salary for a teacher in California is 41,181. assume that this is a normal distribution with a standard deviation of $725. One quarter of starting teachers in California will make how "at least" much money per year? Round to the nearest dollar?

Answer 1

Hi Nicole.

 

It seems your question is asking for the salaries of the top 25% of earners.

 

Using the normal table, we need to look up the z that gives us the 25%.  Since most normal tables give the probability of being less than or equal to z, we want to look up 75% or 0.7500.

 

Using a normal table, for 0.7500, z = 0.675

 

Since Z = (X - μ)/σ

 

Then X, the salary we are looking for

X = Zσ + μ

 

X = (.675) (725) + 41181 = 41670

 

One quarter of the starting teachers in California will make at least $41,670.