Suppose x has a distribution with a mean of 70 and a standard deviation of 12. Random samples of size n = 64 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 = 70 and standard deviation σx = 12. (b) Find the z value corresponding to x = 73. z = (73 - 70) / 12 = 0.25 (c) Find P(x < 73). (Round your answer to four decimal places.) P(x < 73) = 0.5987 (d) Would it be unusual for a random sample of size 64 from the x distribution to have a sample mean less than 73? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 73.
Added by Dustin P.
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When we draw random samples of size n = 64, the mean and standard deviation of the sample mean distribution (also known as the sampling distribution) can be calculated as follows: Mean of the sample mean distribution (μx) = Mean of the population (μ) = Show more…
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