Question

7. If 35% of students get refund on their tax return and we ask 25 students whether they got refunds on their tax returns or not.

a. Define the random variable X

b. List the values X can take on.

c. Give the distribution of X. X __(______,______)

d. How many of the 25 students would we expect to get refunds?

Answer 1

7. If 35% of students get refund on their tax return and we ask 25 students whether they got refunds on their tax returns or not.

Thus probability of succes is 0.35 i.e probability of students get refund .

a. Define the random variable X

Let X be the random variable which can be defined as students getting refund on their tax return .

b. List the values X can take on.

Here we now that either students will get tax returns or will not get tax returns , thus X can take two values

i.e

X = 0          ( if students do not got refunds or if failure )

X = 1          ( if students got refunds or if success )

c. Give the distribution of X. X __(______,______)

Here we know that probability that students get refund is p = 0.35 , thus the probability that students will not get refund will be q = 1-0.35 = 0.65

hence

p = 0.35          ;     q = 0.65

And X is a random varible which can take only two values .

Thus X follows binomial distribution with p = 0.35 probability if success

i.e X ~ B ( n , p = 0.35 )

d. How many of the 25 students would we expect to get refunds?

Since we know that only 35% of students get refund on their tax return i.e p = 0.35

So from n = 25 students , expected students to get refund is 25 * 0.35 = 8.75 9

Or

We know that our random variable X ~ B ( n =25 , p = 0.35 )

Its Expected value is given by

E(X) = n*p

       = 25 * 0.35

E(X) = 8.75 9

Since Expected value is 8.75 , but in praticle 8.75 students is not possible , so we round it off , and conclude that there are aprrox 9 students that we can expect to get refunds .