Question

Suppose that a random sample of size 100 is to be selected from a population with mean 50 and standard deviation 6. (a) What are the mean and standard deviation of the sampling distribution of x? μx = 50 σx = 6 Describe the shape of the sampling distribution of x. Since n is greater than or equal to 30, we can't say what the shape of the distribution of x will be. Since n is greater than or equal to 30, the distribution of x will be approximately normal. Since n is less than 30, the distribution of x will be approximately normal. Since n is less than 30, we can't say what the shape of the distribution of x will be. (b) What is the approximate probability that x will be within 0.3 of the population mean μ? (Round your answer to four decimal places.) (c) What is the approximate probability that x will differ from μ by more than 0.9? (Round your answer to four decimal places.)

          Suppose that a random sample of size 100 is to be selected from a population with mean 50 and standard deviation 6.

(a) What are the mean and standard deviation of the sampling distribution of x?
μx = 50
σx = 6

Describe the shape of the sampling distribution of x.
Since n is greater than or equal to 30, we can't say what the shape of the distribution of x will be. Since n is greater than or equal to 30, the distribution of x will be approximately normal. Since n is less than 30, the distribution of x will be approximately normal. Since n is less than 30, we can't say what the shape of the distribution of x will be.

(b) What is the approximate probability that x will be within 0.3 of the population mean μ? (Round your answer to four decimal places.)

(c) What is the approximate probability that x will differ from μ by more than 0.9? (Round your answer to four decimal places.)

Added by Michael R.

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