A certain chromosome defect occurs in only 1 in 210 adult Ca

A certain chromosome defect occurs in only 1 in 210 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?

Does p have approximately a normal distribution in this case? Explain.

What is the smallest value of n for which the sampling distribution of p is approximately normal

Here,
n =    100
p = 1/210   0.004761905

Hence, the mean is the population proportion,

u = mean = p =    0.004761905   [ANSWER]

sigma = standard deviation = sqrt(p(1-p)/n) =    0.006884206   [ANSWER]

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It is not normally distirbuted, as the ratio of p to sigma (p/sigma = 0.004761905/0.006884206) is less than 3.

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p/sigma = 3

Then

p/sqrt(p(1-p)/n) = 3

p^2 n /(p(1-p)) = 9

n = 9p(1-p)/p^2

As p = 0.004761905

n = 1880.999906 = 1881 [ANSWER]