In a large metropolitan area, past records revealed that 30% of all the high school graduates go to college. from 20 graduates selected at random (n=20), what is the probability that exactly 8 will go to college?

The probability is 0.1144.

Using binomial probability, we have:

[tex]_nC_r\times(p)^r\times(1-p)^{n-r} \\ \\_{20}C_8\times (0.3)^8 \times(1-0.3)^{20-8} \\ \\ \frac{20!}{8!12!}\times (0.3)^8 \times (0.7)^{12} \\ \\=0.1144[/tex]

Answer Link

JeanaShupp JeanaShupp · Answer 2 · 2019-08-13T14:43:13+02:00

Answer: 0.1144

Step-by-step explanation:

Binomial probability formula :-

[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex], P(X) is the probability of getting success in x trials , n is total n umber of trials and p is the probbaility of getting success in each trial.

Given : The proportion of high school graduates go to college : p=0.30

Sample size : n= 20

The probability that exactly 8 will go to college is given by :-

[tex]P(8)=^{20}C_{8}(0.30)^8(0.70)^{12}\\\\=\dfrac{20!}{8!(12)!}(0.3)^8(0.7)^{12}=0.114396739705\approx0.1144[/tex]

Hence, the probability that exactly 8 will go to college = 0.1144