Question

Teachers' salaries in north dakota the average teacher's salary in north dakota is $35,441. assume a normal distribution with s $5100.

a. what is the probability that a randomly selected teacher's salary is greater than $45,000?

b. for a sample of 75 teachers, what is the probability that the sample mean is greater than $38,000?

Answer 1

• a) about 3.0%
• b) about 7×10^-6

Explanation:

These sorts of calculations are best done with a calculator that knows statistics.

a) The z-value of the limit ofv interest is (45,000 -35,551)/(5100) ≈ 1.8743. The empirical rule tells you between 16 and 2.5% of the distribution will lie above a limit that is between 1 and 2 standard deviations. So, our calculator value of 3% is approximately correct.

b) The standard deviation of the sample mean is reduced by a factor of √75 from that of the parent distribution for a sample size of 75. Then the z-value is ...

... (38,000 - 35,441)/(5100/√75) ≈ 2559/588.90 ≈ 4.345

The probability of exceeding this valus is pretty small, about 6.95×10^-6.