approxim ely the sample mean is approximately the sampling distrihurin it says t
ID: 3231114 • Letter: A
Question
approxim ely the sample mean is approximately the sampling distrihurin it says the sampling di ribution R. Ir the sample Mac is of will he normally o, the sampling diseributien only irae individual elements in the underlying population are y irae standard deviation of the yine population ibution itselrki wormally distributed c only if the undert d only irthe populaien mean regardless or the shape of the underlying population dinribution Problem IV. According the US of Justice, 27 N of crimes inthe US 400 erimes a weapon. A sample of crime information for last year in Cedarville indicated 128 eut of or 32% actually involved the use ofa weapon. Department of Justice is uue, what probabilat 27% or more of the the violent in the US involve the use of weapon? 0.4346 20 What is the standard eror erthissampline distributio? 21. What terrobability ofobserving a sample proportionais large er larger? a) 0.0122Explanation / Answer
1
The central limit theorem (CLT) states that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.
The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal if the sample size is large enough.
So option C is correct. VIZ. far any large n, the sampling distribution of the sample mean is approximately normal regardless if the shape of the population.
2.
If the sample size is 10, the sampling distribution of the mean will be normally distributed:
(c) only if the underlying population distribution itself is normally distributed.
Because 10 is a small number. In practice, some statisticians say this number should be around 30 so that the population distribution is roughly bell-shaped.
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