Question

The annual salary of teachers in a certain state has a mean of μ = $ 54,000 and standard deviation of σ = $ 5,000 .

What is the probability that the mean annual salary of a random sample of 5 teachers from this state is more than $60,000?

Answer 1

Solution :

Given that ,

mean = = 54000

standard deviation = = 5000

n = 5

=   = 54000 and

= / n = 5000 / 5 = 2236.0680

P( > 60000) = 1 - P( < 60000)

= 1 - P(( - ) / < (60000 - 54000) / 2236.0680)

= 1 - P(z < 2.68)

= 1 - 0.9963

= 0.0037

Probability = 0.0037

The probability that the mean annual salary of a random sample of 5 teachers from this state is more than $60,000 is 0.0037