A certain chromosome defect occurs in only 1 in 190 adult Caucasian males. A ran

Question

A certain chromosome defect occurs in only 1 in 190 adult Caucasian males. A random sample of n = 100 adult Caucasian males is to be obtained. What is the mean value of the sample proportion p, and what is the standard deviation of the sample proportion? (Enter your mean as an exact integer, fraction, or decimal. Round your standard deviation to five decimal places.) Does p have approximately a normal distribution in this case? Explain. Yes, because np 10. No, because np 10. What is the smallest value of n for which the sampling distribution of p is approximately normal? n = adult Caucasian males

Explanation / Answer

a)here p=1/190

hence as per central limit theorum mean =1/190 =0.00526

and std deviation =(p(1-p)/n)1/2 =0.00724

b) as np =100*1/190<10

hence no becausenp<10

c) the smallest value for which np>10

n*190>10

n>1900

hence for n=1901

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