Find the probability and interpret the results. If convenient, use technology to find the probability. The population mean annual salary for environmental compliance specialists is about $\$ 62,500$. A random sample of 34 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $\$ 58,500$ ? Assume $\sigma=\$ 6,000$. The probability that the mean salary of the sample is less than $\$ 58,500$ is (Round to four decimal places as needed.)

Step 1 ：We are given that the population mean annual salary for environmental compliance specialists is \$62,500, the standard deviation is \$6,000, and a random sample of 34 specialists is drawn from this population. We are asked to find the probability that the mean salary of the sample is less than \$58,500.

Step 2 ：This is a problem of finding the probability of a sample mean in a normally distributed population. We can use the z-score formula to find the z-score of the sample mean, and then use the standard normal distribution to find the probability.

Step 3 ：The z-score formula is: \(z = \frac{X - \mu}{\sigma / \sqrt{n}}\), where \(X\) is the sample mean, \(\mu\) is the population mean, \(\sigma\) is the standard population standard deviation, and \(n\) is the sample size.

Step 4 ：Substituting the given values into the formula, we get \(z = \frac{58500 - 62500}{6000 / \sqrt{34}}\), which simplifies to \(z = -3.887301263230201\).

Step 5 ：After finding the z-score, we can use the standard normal distribution (z-distribution) to find the probability that the z-score is less than the calculated value. This is equivalent to finding the area to the left of the calculated z-score in the z-distribution, which represents the probability.

Step 6 ：The probability calculated is approximately 0.0000506824591217036. This is the probability that the mean salary of the sample is less than \$58,500.

Step 7 ：Final Answer: The probability that the mean salary of the sample is less than \$58,500 is approximately \(\boxed{0.0001}\).