Suppose a random sample of size 49 is drawn from a population with a mean of 279. If 91% of the time the sample mean is less than 283, what is the population standard deviation? (Round your answer to 2 decimal places, e.g. 15.25.) Appendix A Statistica

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**Question:**

Suppose a random sample of size 49 is drawn from a population with a mean of 279. If 91% of the time the sample mean is less than 283, what is the population standard deviation?

(Round your answer to 2 decimal places, e.g., 15.25.)

σ = [ ]

**Explanation:**

This problem requires you to determine the population standard deviation when given the sample size, population mean, and the probability that the sample mean is below a certain value. You can use the properties of the normal distribution and the concept of z-scores to solve it. Refer to Appendix A Statistical Tables for the z-score corresponding to the given probability.
Transcribed Image Text:**Question:** Suppose a random sample of size 49 is drawn from a population with a mean of 279. If 91% of the time the sample mean is less than 283, what is the population standard deviation? (Round your answer to 2 decimal places, e.g., 15.25.) σ = [ ] **Explanation:** This problem requires you to determine the population standard deviation when given the sample size, population mean, and the probability that the sample mean is below a certain value. You can use the properties of the normal distribution and the concept of z-scores to solve it. Refer to Appendix A Statistical Tables for the z-score corresponding to the given probability.
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