Question

The incomes in a certain large population of college teachers have a normal distribution with a mean $75,000 and standard deviation $10,000. 16 teachers are selected at random from this population to serve on a committee. What is the probability that their average salary is more than $77,500?

Answer 1

The probability that their average salary;

standard error

= 10,000/sqrt(16)

=10,000/4

= 2500

(77,500 - 75000)/2500

2,500/2500

= 1

p (z > 1) = .1587

So, the probability that their average salary is more than $77,500 is 0.1587

Explanation: