A school newspaper reporter decides to randomly survey 17 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X.

d. How many of the 12 students do we expert to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend.

Question

Mathematics

Felipe Preston

3 September, 22:21

A school newspaper reporter decides to randomly survey 17 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 23% of students attend Tet festivities. We are interested in the number of students who will attend the festivities. a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X.

d. How many of the 12 students do we expert to attend the festivities?

e. Find the probability that at most four students will attend.

f. Find the probability that more than two students will attend.

+2

Answers (1)

Know the Answer?

Rayne Neal · Answer 1

There is a typing mistake in part (d) of the question. Original question states that total student are 17. In part (d) it asks out of 12 which I think is a mistake as total is 17. Therefore, I am finding the answers with total students as 17. In case if the total is 12 then by just replacing 17 with 12 we can find the answer.

Answer:

All the answers and explanations are given below.

Step-by-step explanation:

(a)

The random variable X will be defined as the number of students who will attend the Tet (Vietnamese New Year) festivities this year.

(b)

As X is the number of students so it can take any value from 0 to 17. This means that when X = 0, 0 student will attend the Tet (Vietnamese New Year) festivities this year. Similarly if X = 17, all 17 students will attend the Tet (Vietnamese New Year) festivities this year. It can only take whole number values because its the number of students.

(c)

X follows Binomial distribution with probability of success = 23% (success defined as attending the festivities).

n = 17 (total number of students)

p = 23% = 0.23 (probability of success)

X ~ Binomial (17, 0.23)

(d)

The number can be found out by n*p

n = 17

p = 0.23

np = 3.91

(e)

Using binomial cdf function in the calculator or any Binomial Probability Calculator online we can find

P (X ≤ 4) = 0.65

This means at most the value can be 4. So the we need to find probability of less than or equal to 4.

(f)

To find probability of more than 2 students we first find probability of less than and equal to 2 students and then subtract it from the total probability which is 1.

P (X ≤ 2) = 0.214

P (X>2) = 1 - 0.214

P (X>2) = 0.786