Suppose x has a distribution with a mean of 40 and a standard deviation of 21. Random samples of size n = 36 are drawn. (a) Describe the distribution. The distribution has an approximately normal distribution. Compute the mean and standard deviation of the distribution. μ = 40 σ = 21/√36 = 3.5 (b) Find the z value corresponding to x̄ = 47. z = (47 - 40) / 3.5 (c) Find P(x < 47). P(x < 47) = P(x̄ < 47) (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 47? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 47.
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