Question

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?

Answer 1

The probability is 0.1144.

Using binomial probability, we have:


`_nC_r*(p)^r*(1-p)^(n-r) \\ \\_(20)C_8* (0.3)^8 *(1-0.3)^(20-8) \\ \\ (20!)/(8!12!)* (0.3)^8 * (0.7)^(12) \\ \\=0.1144`

Answer 2

Answer: 0.1144

Explanation:

Binomial probability formula :-

`P(X)=^nC_xp^x(1-p)^(n-x)`, 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 :-

`P(8)=^(20)C_(8)(0.30)^8(0.70)^(12)\\\\=(20!)/(8!(12)!)(0.3)^8(0.7)^(12)=0.114396739705\approx0.1144`

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