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 $60,500. A random sample of 38 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $58 500? Assume a = $5,800. The probability that the mean salary of the sample is less than $58,500 is (Round to four decimal places as needed.)

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**Title: Calculating Probability in Salary Statistics**

**Problem:**

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 $60,500. A random sample of 38 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $58,500? Assume σ = $5,800.

The probability that the mean salary of the sample is less than $58,500 is _____ (Round to four decimal places as needed.)

**Explanation:**

This problem involves calculating the probability that the sample mean salary is less than a specified amount using the normal distribution. Given the population mean, the sample size, and the standard deviation, we can use statistical methods to find the likelihood of observing such a sample mean. This exercise demonstrates important concepts in inferential statistics, including the application of the Central Limit Theorem.
Transcribed Image Text:**Title: Calculating Probability in Salary Statistics** **Problem:** 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 $60,500. A random sample of 38 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $58,500? Assume σ = $5,800. The probability that the mean salary of the sample is less than $58,500 is _____ (Round to four decimal places as needed.) **Explanation:** This problem involves calculating the probability that the sample mean salary is less than a specified amount using the normal distribution. Given the population mean, the sample size, and the standard deviation, we can use statistical methods to find the likelihood of observing such a sample mean. This exercise demonstrates important concepts in inferential statistics, including the application of the Central Limit Theorem.
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