At a high school with 800 students, 80% of the students ride the school bus. if 20 students are selected randomly (without replacement) and we let x = the number of students in the sample who ride the bus, what is the probability that at least one of the students doesn't ride the bus?

0.9885 (98.85%)

Step-by-step explanation:

Since sample is less than 10% of the population, we can use binomial distribution to approximate the probability.

So we want to calculate P (X < 20).

We can calculate the probability of complement event P (X = 20).

Use binomial formula b (x; n, p) = C (n, x) p^ (x) (1-p) ^ (n-x)

b (20; 20, 0.8)

= C (20, 20) (0.8) ^ (20) (0.2) ^0

= (0.8) ^20 ≈ 0.0115

So since P (X < 20) = 1 - P (X = 20), we have

P (X < 20) ≈ 1 - 0.0115 = 0.9885