The population mean and standard deviation are given belaw. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of n= 65, find the probability of a sample mean being greater than 211 if u = 210 and o=5.8. For a sample of n= 65, the probability of a sample mean being greater than 211 if u = 210 and o = 5.8 is. (Round to four decimal places as needed.)

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The image presents a statistical problem related to finding the probability of a sample mean. Here's a transcription of the text for an educational audience:

---

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

For a sample of \( n = 65 \), find the probability of a sample mean being greater than 211 if \( \mu = 210 \) and \( \sigma = 5.8 \).

For a sample of \( n = 65 \), the probability of a sample mean being greater than 211 if \( \mu = 210 \) and \( \sigma = 5.8 \) is \_\_\_\_. (Round to four decimal places as needed.)

---

To solve this problem, one would typically use the standard normal distribution (z-score) to calculate the probability. The steps usually involve calculating the standard error, finding the z-score, and then using a z-table or statistical software for the probability.
Transcribed Image Text:The image presents a statistical problem related to finding the probability of a sample mean. Here's a transcription of the text for an educational audience: --- The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual. For a sample of \( n = 65 \), find the probability of a sample mean being greater than 211 if \( \mu = 210 \) and \( \sigma = 5.8 \). For a sample of \( n = 65 \), the probability of a sample mean being greater than 211 if \( \mu = 210 \) and \( \sigma = 5.8 \) is \_\_\_\_. (Round to four decimal places as needed.) --- To solve this problem, one would typically use the standard normal distribution (z-score) to calculate the probability. The steps usually involve calculating the standard error, finding the z-score, and then using a z-table or statistical software for the probability.
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