Answer:
The probability that the sample mean is less than $56,000 is 0.0375.
Explanation:
Let <em>X</em> = teacher's salary in Connecticut.
The random variable <em>X</em> follows a Normal distribution with parameters <em>μ</em> = $57,337 and <em>σ</em> = $7,500.
A random sample of <em>n</em> = 100 teacher's salaries are selected.
The sample mean of every sample of 100 salaries will follow a normal distribution with mean <em>μ</em> and standard deviation <em>σ</em>/√n.
Compute the probability that the sample mean of the 100 salaries is less than $56,000 as follows:
*Use a <em>z</em>-table for the probability.
Thus, the probability that the sample mean is less than $56,000 is 0.0375.
