Question

If 28% of students in College are near-sighted, the probability that in a randomly chosen group of 20 College students, exactly 4 are near-sighted is closest to
(A) 17%
(B) 18%
(C) 12%
(D) 16%

Answer 1

Answer: (D) 16%

Step-by-step explanation:

Binomial probability formula :-

$P(x)=^nC_xp^x(1-p)^n-x$, where n is the sample size , p is population proportion and P(x) is the probability of getting success in x trial.

Given : The proportion of students in College are near-sighted : p= 0.28

Sample size : n= 20

Then, the the probability that in a randomly chosen group of 20 College students, exactly 4 are near-sighted is given by :_

$P(x=4)=^{20}C_4(0.28)^4(1-0.28)^{20-4}\\\\=\dfrac{20!}{4!16!}(0.28)^4(0.72)^{16}\\\\=0.155326604912\approx0.16\%$

Hence, the probability that in a randomly chosen group of 20 College students, exactly 4 are near-sighted is closest to 16%.