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 $61,000. A random sample of 43 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $57,500? Assume a = $5,900. The probability that the mean salary of the sample is less than $57,500 is. (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Transcription for Educational Website:**

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**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 $61,000. A random sample of 43 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $57,500? Assume σ = $5,900.

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**The probability that the mean salary of the sample is less than $57,500 is [ ].**

*(Round to four decimal places as needed.)*

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**Explanation:**

This problem involves calculating a probability using the normal distribution. Given the population mean and standard deviation, along with sample size, you would typically standardize the sample mean using the Z-score formula for sample means. This is a standard problem in statistical inference, and often technology or statistical software is used to compute this probability efficiently.
Transcribed Image Text:**Transcription for Educational Website:** --- **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 $61,000. A random sample of 43 specialists is drawn from this population. What is the probability that the mean salary of the sample is less than $57,500? Assume σ = $5,900. --- **The probability that the mean salary of the sample is less than $57,500 is [ ].** *(Round to four decimal places as needed.)* --- **Explanation:** This problem involves calculating a probability using the normal distribution. Given the population mean and standard deviation, along with sample size, you would typically standardize the sample mean using the Z-score formula for sample means. This is a standard problem in statistical inference, and often technology or statistical software is used to compute this probability efficiently.
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