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Suppose x has a distribution with a mean of 60 and a standard deviation of 45. 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 ---Select--- distribution with mean ?_x? = and standard deviation ?_x? = . (b) Find the z value corresponding to x? = 45. z = (c) Find P(x? < 45). (Round your answer to four decimal places.) P(x? < 45) = (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 45? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 45. Yes, it would be unusual because less than 5% of all such samples have means less than 45. Yes, it would be unusual because more than 5% of all such samples have means less than 45. No, it would not be unusual because more than 5% of all such samples have means less than 45.

          Suppose x has a distribution with a mean of 60 and a standard deviation of 45. 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 ---Select--- distribution with mean ?_x? = and standard deviation ?_x? = .
(b) Find the z value corresponding to x? = 45.
z =
(c) Find P(x? < 45). (Round your answer to four decimal places.)
P(x? < 45) =
(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 45? Explain.
No, it would not be unusual because less than 5% of all such samples have means less than 45.
Yes, it would be unusual because less than 5% of all such samples have means less than 45.
Yes, it would be unusual because more than 5% of all such samples have means less than 45.
No, it would not be unusual because more than 5% of all such samples have means less than 45.

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Suppose x has a distribution with a mean of 60 and a standard deviation of 45. 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 —Select— distribution with mean ?x? = and standard deviation ?x? = .
(b) Find the z value corresponding to x? = 45.
z =
(c) Find P(x? < 45). (Round your answer to four decimal places.)
P(x? < 45) =
(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 45? Explain.
No, it would not be unusual because less than 5% of all such samples have means less than 45.
Yes, it would be unusual because less than 5% of all such samples have means less than 45.
Yes, it would be unusual because more than 5% of all such samples have means less than 45.
No, it would not be unusual because more than 5% of all such samples have means less than 45.

Added by Angela G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Joanna Quigley

12/03/2022

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5 (calculated as 45 / √36 = 7.5). Show more…

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Suppose x has a distribution with a mean of 60 and a standard deviation of 45. Random samples of size n = 36 are drawn. (a) Describe the x̅ distribution and compute the mean and standard deviation of the distribution. x̅ has ---Select--- distribution with mean ̄μ_x̄ = and standard deviation σ_x̄ = . (b) Find the z value corresponding to x̅ = 45. z = (c) Find P(x̅ < 45). (Round your answer to four decimal places.) P(x̅ < 45) = (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 45? Explain. No, it would not be unusual because less than 5% of all such samples have means less than 45. Yes, it would be unusual because less than 5% of all such samples have means less than 45. Yes, it would be unusual because more than 5% of all such samples have means less than 45. No, it would not be unusual because more than 5% of all such samples have means less than 45.

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Transcript

00:01 We have a distribution x.

00:03 It has a mean, mu, of 60, and a standard deviation sigma of 45.

00:09 But we're not looking at the original distribution.

00:11 We are taking samples of size 36 and looking at the sampling distribution.

00:18 So if you take every possible sample of size 36 from this population, take the sample means and plot them out.

00:29 You get this.

00:32 It is approximately normal.

00:38 It has a mean equal to the original population.

00:44 So some of your samples will have higher values, some lower, just by chance.

00:48 But the average of the averages is just going to be the same as a population.

00:53 The standard deviation of the sample means is different.

00:58 And the change is sigma over root n.

01:04 So it's going to be 45 divided by root 36.

01:09 45 over 6 is 7 .5.

01:14 There we go.

01:15 How do we know this is approximately normal? because we don't know anything about the shape of the original distribution.

01:21 Well, that is the central limit theorem.

01:25 The central limit theorem states that if you have samples of size at least 30, the sampling distribution is approximately normal.

01:35 And now we can use the normal distribution to answer questions about it.

01:44 So there's the first part, part a, the shape and parameters.

01:49 Part b, the z score for the sample mean of 45.

01:55 So z is equal to x minus mu over sigma.

02:00 It tells you how many standard deviations away from the mean your cutoff point is.

02:05 45 is below the mean here.

02:09 So we want 45 minus 60 divided by 7 .5.

02:14 I'm using these values because we're looking at a sample mean here...

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