Suppose X has a distribution with =72 and a =8 a) If random samples of size n=16

Question

Suppose X has a distribution with =72 and a =8
a) If random samples of size n=16 are selected, can we say anything about the x bar distribution of sample means?

b) If the original X distribution is normal, can we say anything about the x bar distribution of random samples of size 16? Find P(68 < X < 73).

 

Consider two xbar distributions corresponding to the same x distribution. The first xbar distribution is based on sample of  n=100 and the second is based on sample size n=225. Which xbar distribution has the smallest error? Explain

Explanation / Answer

a) We can say that the distribution of the sample mean, based on a random sample of size 16, has mean 72 and standard deviation sqrt(64/16) =2. b) Given the additional assumption of Normality, we can say that the sample mean, based on a random sample of size 16, has a Normal distribution with mean 72 and standard deviation 2. To compute P(68

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