Question

CCA has stated in 2017 that 20.3 % of its students are first generation college students.
Suppose you sample 5 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

b. Give the mean of the binomial distribution. $

c. Give the standard deviation of this binomial distribution.

d. Compute the z-score for the outcome x=1x=1 students are first generation.

Answer 1

CCA has stated in 2017 that 20.3 % of its students are first generation college students.
You sample 5 CCA students and ask if they are first generation college students or not, counting the number of first generation students.
let X be the number of students who are first generation college students.

a) Then X ~ Bin(n, p)

where n=5, p=probability of success (success : being a first generation college student) = 0.203

using this we can calculate the table.

X	P[X=x]
0	0.3216
1	0.4095
2	0.2086
3	0.0531
4	0.0068
5	0.0003

b) mean of the binomial distribution = n*p= 5*0.203= 1.015

c) variance of this binomial distribution = n*p*(1-p) = 5*0.203*0.797= 0.809

standard deviation =

d)

so,

for X=1, z-score is :