Question

1. Yale Law School says 74% of their students pass the bar exam on their first try.

1. To simulate passing students, we could assign the random digits as:
   1. 00 to 49 = pass first try, 50 to 99 = fail first try
   2. 0 to 7 = pass first try, 8 to 9 = fail first try
   3. 00 to 73 = pass first try, 74 to 99 = fail first try
   4. 0 to 4 = pass first try, 5 to 9 = fail first try

Using the random digit assignment from part a), and starting at line 106 simulate a class of 20 students.

Student	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20
Random digit
Pass or fail

                             

b) Which students was the first in the list to fail the exam?

c) What percentage of these 20 students passed on their first try?

4. How does that percentage compare to 74% we set up as our probability model? If there is a difference, why do you think that is?

Answer 1

(a)

To simulate we have to assign random numbers in such a manner that out of all possible random numbers, 74% corresponds to pass in first try and (100-74)%=26% corresponds to fail in first try.

Hence, we could assign the random digits as (C) 00 to 73 = pass first try, 74 to 99 = fail first try.

A random number table with line 106 is as follows.

We take random numbers consisting of two digits and perform simulation as follows.

Student	Random number	Pass/Fail	Student	Random number	Pass/Fail
1	36	Pass	11	80	Fail
2	85	Fail	12	33	Pass
3	59	Pass	13	56	Pass
4	01	Pass	14	46	Pass
5	62	Pass	15	86	Fail
6	96	Fail	16	91	Fail
7	77	Fail	17	38	Pass
8	48	Pass	18	85	Fail
9	68	Pass	19	15	Pass
10	15	Pass	20	50	Pass

(b)

Student 2 is the first in the list to fail in the exam.

(c)

Out of 20 students, 13 passed in the first try.

So, percentage of students passed on their first try = 13*100/20% = 65%

(d)

There is a difference. This difference occurs due to sampling. With increase in sample size this percentage will approach to 74.