Question

The average teacher salary in Nebraska is $52,925 with a standard deviation of $12,115. We collect a random sample of 50 Nebraska teachers and record their salary.

Part 1: (6 pts) Check all necessary conditions in detail (not just yes or no) and give the sampling model and parameters to the nearest dollar.

Part 2: (6 pts) What is the probability that the average teacher salary in our sample of 50 teachers is less than $50,000? Find the z-score and probability. Be sure you use the appropriate p-value notation!

Then write a sentence that summarizes your results.

Answer 1

Part 1:

The conditions are:

The data follow the normal probability distribution.

The sample is a simple random sample from its population.

Each individual in the population has an equal probability of being selected in the sample.

The sampling distribution is:

µx = 55925

σx = σ/√n = 12115/√50 = 1713.32

Part 2:

z = (x - µ)/σ/√n

z = (50000 - 55925)/12115/√50

z = -3.46

P (z < -3.46) = 0.0003

The probability that the average teacher salary in our sample of 50 teachers is less than $50,000 is 0.0003.