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/√100 = 0.6
Describe the shape of the sampling distribution of x.
a. Since n is less than 30, the distribution of x will be approximately normal.
b. Since n is greater than or equal to 30, the distribution of x will be approximately normal.
c. Since n is less than 30, we can't say what the shape of the distribution of x will be.
d. Since n is greater than or equal to 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 0.4 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 0.8? (Round your answer to four decimal places.)