Question

Thirty percent of students graduate from high school before they reach the age of 18. In a random sample of 16 high-school graduates, what is the probability that:

**use binomial table** I just want to check that my answers are right? Having trouble with the last question though....

a. more than 10 of them graduated before they were 18 years old?

P(x > 10)

=P(x=11)+P(x=12)+ - - - +P(x=16)

=0.0013+0.0002+0.0000+0.0000+0.0000+0.0000

=0.0015

The probability that more than 10 will graduate before 18 is 0.0015

b. at most 4 of them graduated before they were 18?

P(at most 4)= P(x=0)+P(x=1)+P(x=2)+P(x=3)+P(x=4)

P(x < 4)=0.0033+0.0228+0.0732+0.1465+0.2040

=0.4498

The probability that at most 4 will graduate before 18 is 0.4498

c. fewer than 7 of them graduated after they turned 18?

Answer 1

Let X denote the number of students who graduate from high school before they reach the age of 18

n = 16, p = 0.30

(a) The required probability = P(X > 10)

= 1 - binomcdf(16, 0.3, 10)

= 0.0016

(b) The required probability = P(X ≤ 4)

= binomcdf (16, 0.3, 4)

= 0.4499

(c) Fewer than 7 graduated after they turned 18 -> Greater than 9 graduated before they reach the age of 18

Thus, the required probability = P(X > 9)

= P(X = 10) + P(X > 10)

= 0.0055 + 0.0016

= 0.0071