Question

1. A teacher has taken attendance of her class of five students for the entire semester and found the number of days with each level of attendance. Her records show the following:

                                     # of Students attending class: 1      2      3     4      5

Days in the semester with this attendance level (out of 30 days):            4      2     10    4     10

a) What’s the probability of there being 3 or more students on any random day?

b) What is the expected number of students to attend a randomly selected day?

Answer 1

Solution:

From the given data, we have

x	f(x)	P(x)	F(x)
1	4	0.1333	0.1333
2	2	0.0667	0.2000
3	10	0.3333	0.5333
4	4	0.1333	0.6667
5	10	0.3333	1.0000
Total	30	1.0000

a) What’s the probability of there being 3 or more students on any random day?

Here, we have to find P(X≥3)

P(X≥3) = 1 – P(X≤2)

P(X≥3) = 1 – 0.2000

P(X≥3) = 0.8000

Required probability = 0.8000

b) What is the expected number of students to attend a randomly selected day?

Expected number of students = E(x)

E(x) = ∑x*f(x)/∑f(x)

The calculation table is given as below:

x	f(x)	x*f(x)
1	4	4
2	2	4
3	10	30
4	4	16
5	10	50
Total	30	104

E(x) = 104/30 = 3.466667

Expected number of students = 3.47