Suppose x has a distribution with a mean of 90 and a standard deviation of 3. Random samples of size n = 36 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. x has a normal distribution with mean μx = 90 and standard deviation σx = 3. (b) Find the z value corresponding to x = 91. z = (91 - 90) / 3 = 0.3333. (c) Find P(x < 91). P(x < 91) = 0.6306. (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 91? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 91.
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(a) The x distribution is a normal distribution with a mean (μx) of 90 and a standard deviation (σx) of 3. Show more…
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