Suppose that a random sample of size 64 is to be selected from a population with

Question

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? (Round the answer to three decimal places.) mu^-_x = sigma^-_x = (b) What is the approximate probability that x will be within 0.4 of the population mean mu? (Round the answer to four decimal places.) (c) What is the approximate probability that x will differ from mu by more than 0.6? (Round the answer to four decimal places.)

Explanation / Answer

a) sample mean = population mean .

sample variance = poulation variance /sample size. so here variance= 25/65. std deviation is sq root of variance.

b) assume that the variable follows normal distribution. then probability of ( 39.6<x-bar<40.4). where x-bar follows normal distribution with mean and sd 40 and 0.625 respectively. can be done using any softwere or using biometrika table.

c)similarly calculate p(39.4<x-bar<40.6)

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