Question

Suppose that we will randomly select a sample of 81 measurements from a population having a mean equal to 21 and a standard deviation equal to 6. (a) Describe the shape of the sampling distribution of the sample mean x? . Do we need to make any assumptions about the shape of the population? Why or why not? Normally distributed ; no , because the sample size is large (b) Find the mean and the standard deviation of the sampling distribution of the sample mean x? . (Round your ?x? answer to 1 decimal place.) ?x? 21 ?x? 81.0 (c) Calculate the probability that we will obtain a sample mean greater than 22; that is, calculate P( x? > 22). Hint: Find the z value corresponding to 22 by using ? x? and ? x? because we wish to calculate a probability about x? . (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.) P(x? > 22) (d) Calculate the probability that we will obtain a sample mean less than 20.458; that is, calculate P( x? < 20.458) (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.) P(x? < 20.458)

          Suppose that we will randomly select a sample of 81 measurements from a population having a mean equal to 21 and a standard deviation equal to 6.

(a) Describe the shape of the sampling distribution of the sample mean x? . Do we need to make any assumptions about the shape of the population? Why or why not?
Normally distributed ; no , because the sample size is large

(b) Find the mean and the standard deviation of the sampling distribution of the sample mean x? . (Round your ?x? answer to 1 decimal place.)
?x? 21
?x? 81.0

(c) Calculate the probability that we will obtain a sample mean greater than 22; that is, calculate P( x? > 22). Hint: Find the z value corresponding to 22 by using ? x? and ? x? because we wish to calculate a probability about x? . (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)
P(x? > 22)

(d) Calculate the probability that we will obtain a sample mean less than 20.458; that is, calculate P( x? < 20.458) (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)
P(x? < 20.458)

Suppose that we will randomly select a sample of 81 measurements from a population having a mean equal to 21 and a standard deviation equal to 6.

(a) Describe the shape of the sampling distribution of the sample mean x? . Do we need to make any assumptions about the shape of the population? Why or why not?
Normally distributed ; no , because the sample size is large

(b) Find the mean and the standard deviation of the sampling distribution of the sample mean x? . (Round your ?x? answer to 1 decimal place.)
?x? 21
?x? 81.0

(c) Calculate the probability that we will obtain a sample mean greater than 22; that is, calculate P( x? > 22). Hint: Find the z value corresponding to 22 by using ? x? and ? x? because we wish to calculate a probability about x? . (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)
P(x? > 22)

(d) Calculate the probability that we will obtain a sample mean less than 20.458; that is, calculate P( x? < 20.458) (Use the rounded standard error to compute the rounded Z-score used to find the probability. Round your answer to 4 decimal places. Round z-scores to 2 decimal places.)
P(x? < 20.458)

Added by Elijah P.

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