A study reports that 36% of the companies in Country A have three or more female

Question

A study reports that 36% of the companies in Country A have three or more female board directors. Suppose you select a random sample of 100 respondents. What is the probability that the sample will have between 28% and 45 % of comanies in Country A that have three or more female board directors, the probability is 90% tat the sample percentage of Country A companies having three or more femal board directors will be contained within what symmetrical limits of the population percentage: the probability is 90% that the sample percentage will be contained above(____%) and below (_____%). The probability is 99.7% that the sample percentage of Country A companies having three or more femail board directors will be contained within what symmetrical limits of the population percentage: the sample percentage will be contained above(____%) and below (____%)

Explanation / Answer

here p=0.36 and n=100

for std error of mean =(p(1-p)/n)1/2 =0.048

hence P(0.28<X<0.45)=P((0.28-0.36)/0.048<z<(0.45-0.36)/0.048)=P(-1.667<z<1.875)=0.9696-0.0478 =0.9218

for 90% ; z=1.645

hence 90% that the sample percentage will be contained above (36-1.645*4.8=28.10) % and below (36+1.645*4.8=43.90)%

for 99.7% ; z=2.9677

hence 90% that the sample percentage will be contained above (36-2.9677*4.8=21.75) % and below (36+2.9677*4.8=50.25)%

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