Question

Assume that the salaries of elementary school teachers in the U.S are normally distributed with a mean of $35,000 and a standard deviation of $4000. What is the cutoff salary for teachers in the top 30%

Answer 1

Given that,

mean = = $35000

standard deviation = =$4000

Using standard normal table,

P(Z > z) = 30%

= 1 - P(Z < z) = 0.30

= P(Z < z ) = 1 - 0.30

= P(Z < z ) = 0.30

= P(Z <0.524) = 0.70

z = 0.524 (using standard normal (Z) table )

Using z-score formula  

x = z * +

x= 0.524 *4000+35000

x= 37096