Question

The Statistical Abstract of the United States reported that 66% of students who graduated from high school in a recent year enrolled in college. Thirty high school students where sampled. Round each of the following values to 4 decimal places. a. What is the probability that exactly 18 of them enroll in college? b. What is the probability that more than 15 of them enroll in college? c. Would it be unusual for fewer than 12 of them to enroll in college?

Answer 1

number of students selected =n=30

Probability that a student enrolled in the college=p=0.66

let X is number of student enrolled in the college out of n selected students

X~Bin(30,0.66)

so

$P(X=x)=\binom{30}{x}0.66^x(1-0.66)^{30-x},x=0,1,2,...,30$

a)

we have to find P(X=18)

now

$P(X=x)=\binom{30}{18}0.66^{18}(1-0.66)^{30-18}=0.1166$

b)

we have to find P(X>15)

now

$P(X>15)=P(X\geq 16)=\sum_{x=16}^{30}\binom{30}{18}0.66^{x}(1-0.66)^{30-x}=0.9486$

c)

we have to find P(X<12)

now

$P(X<12)=P(X\leq 11)=\sum_{x=0}^{11}\binom{30}{18}0.66^{x}(1-0.66)^{30-x}=0.0010$

yes probability of getting less than 12 students enrolled is very low so its unusual