Question

Suppose x has a distribution with a mean of 60 and a standard deviation of 27. Random samples of size n = 36 are drawn. USE SALT (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? = 64.5. z = (c) Find P(x? < 64.5). (Round your answer to four decimal places.) P(x? < 64.5) = (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 64.5? Explain. Yes, it would be unusual because more than 5% of all such samples have means less than 64.5. No, it would not be unusual because less than 5% of all such samples have means less than 64.5. No, it would not be unusual because more than 5% of all such samples have means less than 64.5. Yes, it would be unusual because less than 5% of all such samples have means less than 64.5.

          Suppose x has a distribution with a mean of 60 and a standard deviation of 27. Random samples of size n = 36 are drawn.
USE SALT
(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? = 64.5.
z =
(c) Find P(x? < 64.5). (Round your answer to four decimal places.)
P(x? < 64.5) =
(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 64.5? Explain.
Yes, it would be unusual because more than 5% of all such samples have means less than 64.5.
No, it would not be unusual because less than 5% of all such samples have means less than 64.5.
No, it would not be unusual because more than 5% of all such samples have means less than 64.5.
Yes, it would be unusual because less than 5% of all such samples have means less than 64.5.

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Suppose x has a distribution with a mean of 60 and a standard deviation of 27. Random samples of size n = 36 are drawn.
USE SALT
(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? = 64.5.
z =
(c) Find P(x? < 64.5). (Round your answer to four decimal places.)
P(x? < 64.5) =
(d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 64.5? Explain.
Yes, it would be unusual because more than 5% of all such samples have means less than 64.5.
No, it would not be unusual because less than 5% of all such samples have means less than 64.5.
No, it would not be unusual because more than 5% of all such samples have means less than 64.5.
Yes, it would be unusual because less than 5% of all such samples have means less than 64.5.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

11/04/2022

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Step 1: Describe the x distribution and compute the mean and standard deviation of the distribution x has. Show more…

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Suppose x has a distribution with a mean of 60 and a standard deviation of 27. Random samples of size n = 36 are drawn. (a) Describe the x̄ distribution and compute the mean and standard deviation of the distribution. x̄ has distribution with mean μ_x̄ = and standard deviation σ_x̄ = . (b) Find the z value corresponding to x̄ = 64.5. z = (c) Find P(x̄ < 64.5). (Round your answer to four decimal places.) P(x̄ < 64.5) = (d) Would it be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 64.5? Explain. Yes, it would be unusual because more than 5% of all such samples have means less than 64.5. No, it would not be unusual because less than 5% of all such samples have means less than 64.5. No, it would not be unusual because more than 5% of all such samples have means less than 64.5. Yes, it would be unusual because less than 5% of all such samples have means less than 64.5.

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Transcript

00:01 Hi, i'm david and i'm here to help you and see your question.

00:03 In the question here, we are going to discuss about the sampler distribution on the sample mean.

00:08 Let me remind you that if you have the sample size n -queter equal to the 30, and then by the center limit theorem, the sum of mean x -bound will be approximately to the normal.

00:20 Where we have the mean on the x -par equal to the mean of the population, standard difference x -par equals the sigma defined with square the n.

00:28 And because it follows by the normal, if we take the x bar will minus the mean or with the standard deviation, we obtain the standard normal.

00:37 In this question here, we're given the mean equal to the 60 and the standard deviation equal to the 27.

00:45 The sample size is equal to the 36, so it's greater than 30 already.

00:50 Now in the first question 8, we will describe the x bar with approximately to the normal, with the mean of the xbore equal to the mean of the population and equal to the 60 standard division x bar it would equal to sigma divinely square n equal to the 27 25 square root 36 equal to the 27 over 6 and then we get equal to 2 .5 and then for the question b i want to find the g score of the x bar equal to the sixty four point five then for the z of this one equal to by the formula here and get equal to the sixty four point five minus the mean will be the sixty over the standard deviation and then we have equal to exactly one and for the question c want to found the probability done x -bile will be smaller than the 64 .5.

02:04 And to find this probability, we convert the x -1 into the z, and the g -scrom, the 64 .5 equals to the 1...

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