Suppose x has a distribution with a mean of 55 and a standard deviation of 18. Random samples of size n = 81 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. (b) Find the z value corresponding to x = 52. (c) Find P( < 52). (d) Would it be unusual for a random sample of size 81 from the x distribution to have a sample mean less than 52? Explain.

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Tutorial Exercise
Suppose x has a distribution with a mean of 55 and a standard deviation of 18. Random samples of size
n = 81 are drawn.
(a) Describe the x distribution and compute the mean and standard deviation of the distribution.
(b) Find the z value corresponding to x = 52.
(c) Find P(x < 52).
(d) Would it be unusual for a random sample of size 81 from the x distribution to have a sample mean
less than 52? Explain.
Step 1
(a) Describe the x distribution and compute the mean and standard deviation of the distribution.
The central limit theorem states that when the sample size n is 30 or larger, the x distribution is
approximately normal. Here we are given n = 81 and since 81 > 30 we can say that the x distribution is
approximately normal.
We are given that the x distribution has mean 55. Since the distribution is approximately normal we have
H =
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Transcribed Image Text:Tutorial Exercise Suppose x has a distribution with a mean of 55 and a standard deviation of 18. Random samples of size n = 81 are drawn. (a) Describe the x distribution and compute the mean and standard deviation of the distribution. (b) Find the z value corresponding to x = 52. (c) Find P(x < 52). (d) Would it be unusual for a random sample of size 81 from the x distribution to have a sample mean less than 52? Explain. Step 1 (a) Describe the x distribution and compute the mean and standard deviation of the distribution. The central limit theorem states that when the sample size n is 30 or larger, the x distribution is approximately normal. Here we are given n = 81 and since 81 > 30 we can say that the x distribution is approximately normal. We are given that the x distribution has mean 55. Since the distribution is approximately normal we have H = Submit Skip (you cannot come back).
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