Question

The average teachers' salary in a certain state is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7500. Assume that the sample is taken from a large population and the correction factor can be ignored. Use a TI-83 Plus/TI-84 Plus calculator and round the answer to at least four decimal places.What is the probability that a randomly selected teacher makes less than $50,000 per year?

Answer 1

Normal distribution of salaries

d = Standard dev = $7500 =

Correction factor= 0

Di

f(x) = (1/ d•√2π )• e ^- ((s- s')^2/2d^2)

Average value = u = 57337

Now calculate f(x)

Difference of salaries ,with respect to average

S^ 2= 57337 - 50000= = 7337

Now squared = (7337^2) = 53831569

d = 7500

2•d^2= 112500000

Then

S^2/ (2•d^2) = 53831569/112500000= 0.4785

Then now calculate

f(x) = (1/ d•√2π )•e^- (0.4785)

f(x)= 0.619/ (2•d^2)

Answer is

Probability of 61.9%