In 2010, the average overall SAT score (Critical Reading, Math, and Writing) for

Question

In 2010, the average overall SAT score (Critical Reading, Math, and Writing) for college-bound students in the United States was 1509 out of 2400. Suppose that 35% of all high school graduates took this test, and that 300 high school graduates are randomly selected from throughout the United States. Which of the following random variables has an approximate binomial distribution? If possible, give the values for n and p. (If not possible, enter IMPOSSIBLE.)

(a) The number of students who took the SAT.

This is a binomial random variable.This is not a binomial random variable.    

(b) The scores of the 300 students on the SAT.

This is a binomial random variable.This is not a binomial random variable.    

(c) The number of students who scored above average on the SAT.

This is a binomial random variable.This is not a binomial random variable.    

(d) The amount of time it took the students to complete the SAT.

This is a binomial random variable.This is not a binomial random variable.    

Explanation / Answer

let p denotes the 35% of all high school graduates took this test.

p=0.35

let n denotes the number of high school graduates

n=300

a)let x denotes the number of students who took the SAT.the random varaible x follows binomial distribution .

because the random variable x satisfies the following conditions.

the experiment consists of 300 graduates , n=300

this experiment consists two possible cases.that is who took the SAT test , not took SAT test

p=0.35

the events are independent.

b)

there is no information about this random varaible.

so it does not follows binomial distribution.

c)

there is no information about this random varaible.

so it does not follows binomial distribution

d)

there is no information about this random varaible.

so it does not follows binomial distribution

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