Question

Let X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 210 ft and standard deviation 18.6 ft. You intend to measure a random sample of n = 108 trees. The bell curve below represents the distibution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places. 4 = =

Answer 1

Formulas: 1) Ifu, o are the mean and standard deviation of the population. If we take n samples out of the population then sample mean is My = u and sample standard deviation is og vn Šis sample mean(Sample average) random variable. According to central limit theorem, follows normal distribution irrespective of the distribution of X if sample size (n) > 30 In our problem, sample size = n = 108 > 30 Therefore, sample mean follows normal distribution.

Sample size = n = 108 Mg = M = 210 18.6 Oj 1.79 V108 Mg – 20 3 = 210 – 2 * 1.79 = 206.42 Mx + 20 g = 210 + 2 * 1.79 = 213.58 210 0:- 1.79 206.42210 213.58

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