Question

Use the student dataset for this question. students are considered “full-time” students if they are enrolled in 12 or more credits in a given semester. 

What percent of respondents in the student dataset are “full-time” students? Consider your result to part (a) as the best estimate for the probability of any randomly selected student being full-time. Based on that response, what is the probability that in a class of 20 students they will all be full-time?

 

Credits
13
12
6
9
15
9
15
15
13
16
15
10
12
16
15
10
13
15
6
13
7
9
12
13
16
8
4
10
13
15
12
13
3
10
13
16
12
10
14
13

Answer 1

From the data we can see that there are 26 students enrolled in 12 or more credits in a semester       
Total number of students = 40       
a) Let p = proportion of students from the respondents that are full-time students       
p = 26/40 = 0.65 = 65%       
Percent of respondents in the student dataset are “full-time” students = 65%       
        
b) n = 20 sample class of 20 students      
p = 0.65 best estimate for probability of randomly selected student being full-time      
Let X be the number of students being full-time in the class of 20 students       
X ~ Binomial distribution with n = 20 and p = 0.65       
To find P(X=20)       
We use the Excel function BINOM.DIST to find the probability       
P(X=20) = BINOM.DIST(20,20,0.65,FALSE)       
                 = 0.000181       
P(in a class of 20 students they will all be full-time) = 0.000181