Question

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?

Answer 1

Answer:

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