Chapter 6--Problem 14, A normal distribution has a u = 80 and a= 20. For each of

Question

Chapter 6--Problem 14, A normal distribution has a u = 80 and a= 20. For each of the following scores, indicate whether the tailsof the distribution is located to the right or the left of thescore, and find the proportion of the distribution located in thetail. A. X = 85 B. X = 92 C. X = 70 D. X = 64

Chapter 7- Problem 4, The distribution of sample means is notalways a normal distribution. Under what circumstances will thedistribution of sample means not be normal?

Explanation / Answer

Tail is to the left if X mean. A) z(85) = (85 - 80) / 20 = .25 --> p = .5987 --> tail = 1-.5987 = .4013 B) z(92) = (92 - 80) / 20 = .60 --> p = .7257 --> tail = 1 -.7257 = .2743 C) z(70) = (70 - 80) / 20 = -.5 --> p = .3085 --> tail =.3085 D) z(64) = (64 - 80) / 20 = -.8 --> p = .2119 --> tail =.2119 The distribution of a sample mean is normal if population your aresampling is normal. It approximates a normal distribution ifyou sample enough elements and the distribution is "similar" to anormal distribution (i.e. it isn't something that looks totallydifferent). If you have a small sample size and yourdistribution does not resemble a normal distribution, then thedistribution of means will not be normal. For instance, if your sample size is 1 and your distribution islognormal, then your distribution of means will clearly belognormal as the average of 1 element is just itself.

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