Suppose that a random sample of size 64 is to be selected from a population with mean 40 and standard deviation 5. (a) What are the mean and standard deviation of the sampling distribution? μx = σx = (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.) P = (c) What is the approximate probability that x will differ from μ by more than 0.6? (Round your answer to four decimal places.)

a) 0.625

b) 0.2510

c) 0.2005

Step-by-step explanation:

Data provided in the question:

Sample size, n = 64

Mean = 40

Standard deviation = 5

a) Mean of the sampling distribution = Sample mean = 40

Standard deviation of the sampling distribution =

=

= 0.625

b)

(from standard normal table)

c)

(from standard normal table)

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