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. (6 pts) 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

Solution

p = 1/210

n=100

Mean value of the sample proportion = n*p = 100 * 1/210 = 0.476 Answer

SD of the sample proportion = sqrt(n*p*(1-p)) = sqrt(100*(1/210)*(1-1/210)) = 0.688 Answer

For smallest value of n ,

np>5,

so n=5/p

=5*210

=1050 Answer