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