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07 Dec 2018, 07:16
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Of 500 students in a high school, 72 % have indicated that they are interested in attending college. What is the probability of selecting a random sample of 50 students wherein the sample proportion indicating interest in college is greater than 80 %?
10 Dec 2018, 07:08
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Number of students interested in attending college \(= \frac{72}{100}*500 =360\)
Total number of ways of selecting 50 students out of 500 \(= C(500,50) = \frac{500!}{450!50!}\) ...(1)
Number of ways of selecting 50 students such that proportion indicating interest in college is greater than 80 %
\(=C(360,41)*C(140,9)+C(360,42)*C(140,8)+C(360,43)*C(140,7)+C(360,44)*C(140,6)+C(360,45)*C(140,5)+C(360,46)*C(140,4)+C(360,47)*C(140,3)+C(360,48)*C(140,2)+C(360,49)*C(140,1)+C(360,50)*1\)
...(2)
Dividing (2) by (1), we will get the required probability.
