Question

The average teacher's salary in Connecticut (ranked first among states) is $57,337. Suppose that the distribution of salaries is normal with a standard deviation of $7,500. If we sample 100 teachers' salaries, what is the probability that the sample mean is less than $56,000.

Answer 1

Answer:

The probability that the sample mean is less than $56,000 is 0.0375.

Explanation:

Let X = teacher's salary in Connecticut.

The random variable X follows a Normal distribution with parameters μ = $57,337 and σ = $7,500.

A random sample of n = 100 teacher's salaries are selected.

The sample mean of every sample of 100 salaries will follow a normal distribution with mean μ and standard deviation σ/√n.

Compute the probability that the sample mean of the 100 salaries is less than $56,000 as follows:

$P(\bar X$

*Use a z-table for the probability.

Thus, the probability that the sample mean is less than $56,000 is 0.0375.