Decimals mentioned are important (a) A random sample of n = 50 couples will be s

Question

Decimals mentioned are important (a) A random sample of n = 50 couples will be selected from this population and p, the proportion of couples that are mixed racially or ethnically, will be computed. What are the mean and standard deviation of the sampling distribution of p? (Round your standard deviation to four decimal places.) mean .09 standard deviation 0.0016 (b) Is it reasonable to assume that the sampling distribution of p is approximately normal for random samples of size n 50? Explain. O Yes, because np 10 and n(1 -p)> 10. No, because np 10 (c) Suppose that the sample size is n = 200 rather than n = 50, as in Part (b). Does the change in sample size change the mean and standard deviation of the sampling distribution of p? What are the values for the mean and standard deviation when n = 2007( Round your standard deviation to four decimal places.) mean standard deviation (d) Is it reasonable to assume that the sampling distribution of p is approximately normal for random samples of size n = 200? Explain. O Yes, because np 10 No, because np 10o (e) when n = 200, what is the probability that the proportion of couples in the sample who are racially or ethnically mixed will be greater than 0.12? (Round your answer to four decimal places.)

Explanation / Answer

a) mean =0.09

std deviation =(p(1-p)/n)1/2 =0.0404

b) No because np<10

c)mean =0.09

std deviation =(p(1-p)/n)1/2 =0.0202

d)Yes because np>10

e) P(X>0.12)=P(Z>(0.12-0.09)/0.0202)=P(Z>1.4825)=0.0691 ( please try 0.0688 if this does not work)

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