Question

Approximate the following binomial probability by the use of normal approximation. Twenty percent of students who finish high school do not go to college. What is the probability that in a sample of 80 high school students, 10 or less will not go to college? (Enter as a decimal rounding to 3 decimal places)

Answer 1

Title:

The answer is ∑$^{80}C_r \times (\frac{1}{5} )^r \times (\frac{4}{5} )^{80 - r}$, where r = 0, 1, ....10. The value is 0.02010 ≅ 0.020.

Step-by-step explanation:

It is given that, among 100 students, 20 students who finish high school, do not go to college.

Hence, the probability that a student will not go to school is $\frac{20}{100} = \frac{1}{5}$.

We need to find the probability that 10 or less than 10 will not go to college.

The probability that all will go to college is $(1 - \frac{1}{5} )^{80} = (\frac{4}{5} )^{80}$.

The probability that only one will not go to college is $^{80}C_1 \times \frac{1}{5} \times(\frac{4}{5} )^{79}$.

Similarly, the probability of 10 or less than 10 will not go to college can be shown by ∑$^{80}C_r \times (\frac{1}{5} )^r \times (\frac{4}{5} )^{80 - r}$, where r = 0, 1, ....10.