Question

CCA has stated in 2017 that 37.5 % of its students are first generation college students.
Suppose you sample 15 CCA students and ask if they are first generation college students or not, counting the number of first generation students.

a. Create a binomial probability distribution (table) for this situation.

(Report answers accurate to 4 decimal places.)

k	P(X = k)
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

a. What is the probability that 11 students or less are first generation?


b. What is the probability that at least 7 students are first generation ?


c. What is the probability that 4 students will be first generation?


d. What is the probability that between 7-14 students are first generation (inclusing 7 and 14)?


e. What is the probability that 7 students are NOT first generation?

Answer 1

a) Binomial probability distribution (table) with parameters n=15 and p=0.375.

where P(X=k) = ⁿC_k p^k (1-p)^(n-k)

k	P(x=k)
0	0.0009
1	0.0078
2	0.0328
3	0.0852
4	0.1534
5	0.2025
6	0.2025
7	0.1562
8	0.0937
9	0.0437
10	0.0157
11	0.0043
12	0.0009
13	0.0001
14	0.0000
15	0.0000
Total	1.0000

a. What is the probability that 11 students or less are first generation?

Ans:Required probability =


b. What is the probability that at least 7 students are first generation ?

Ans:Required probability =

c. What is the probability that 4 students will be first generation?

Ans:Required probability =

d. What is the probability that between 7-14 students are first generation (inclusing 7 and 14)?
Ans:Required probability =


e. What is the probability that 7 students are NOT first generation?

Ans:Required probability =P( 7 students are NOT first generation)= 1-P( 7 students are first generation)