The following directions apply to problems 11 and 12. Use the Standard Normal Ta

Question

The following directions apply to problems 11 and 12. Use the Standard Normal Table to find the z-score that corresponds to the given cumulative area. If the area is not in the table, use the entry closest to the area. If the area is halfway between two entries, use the z-score halfway between the corresponding z-scores. 11. Area = 0.9808 12. Area = 0.0271 13. Find the z-score that has 61.4% of the distribution’s area to its right. Section 5.4 Problems 14 and 15. Use the following information to answer the questions. A population with n = 373 has a mean µ = 97 and a standard deviation = 8. 14. Find the mean of the sampling distribution of the sample means. 15. Find the standard deviation of the sampling distribution of the sample means. 16. True or False? According to the Central Limit Theorem, if a sample of any size is taken from a population that follows a normal distribution, then the sampling distribution of the sample means will be normally distributed. Please show details.Thanks

Explanation / Answer

11. Using Standard Normal Table find the z-score that corresponds to the given cumulative area 0.9808 is 2.07.

12.Using Standard Normal Table find the z-score that corresponds to the given cumulative area 0.0271 (or 0.0274) is -1.92.

14.The mean of the sampling distribution of the sample means is same as population mean mu=97.

Using central limit theorem the sampling distribution of sample means follows normal distribution with mean mu and standard deviation sigma/root over n.

15.The standard deviation is sigma/root over n=8/root over 373=0.41

16.The given statement is false. The central limit theorem (CLT) states that, given certain conditions, the mean of a sufficiently large number of iterates of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normal, regardless of the underlying distribution.

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