Question

The average teacher’s salary is $45,000. Assume a normal distribution with standard deviation equal to $10,000. a) What is the probability that a randomly selected teacher makes greater than $65,000 a year? b) If we sample 100 teachers’ salaries, what is the probability that the sample mean will be greater than $65,000?

Answer 1

a)

Given,

= 45000 , = 10000

We convert this to standard normal as

P( X < x) = P( Z < x - / )

So,

P( X > 65000) = P( Z > 65000 - 45000 / 10000)

= P( Z > 2)

= 0.0228 (Probability calculated from Z table)

b)

Using central limit theorem,

P( < x) = P (Z < x - / / sqrt(n) )

So,

P( > 65000) = P( Z > 65000 - 45000 / 10000 / sqrt(100) )

= P( Z > 20)

= 0