Question

The mathematics department is considering revising how statistics is taught. In order to see if their changes will be effective in increasing student performance, they decided to run a Simulated Experiment. Previous semesters have that 10% of students receive an A in the class, 40% receive a B, and 20% receive a C. How would you assign values so you can use a Random Digit Table to run this experiment?

a) Assign 1 digit numbers as follows: 0 is A; 1, 2, 3, 4 are B; 5, 6 are C; 7, 8, 9 are D.

b) Assign 1 digit numbers as follows: 0 is A; 1, 2, 3, 4 are B; 5, 6 are C; 7, 8, 9 are other grades.

c) Assign 2 digit numbers as follows: 00-10 are A; 00-40 are B; 0-20 are C.

d) Assign 2-digit numbers as follows: 90-99 are A; 80-89 are B; 70-79 are C; 60-69 are D; and 00-59 are F.

e) This experiment cannot be simulated using a random digit table.

Answer 1

Previous semesters have that 10% of students receive an A in the class, This is same as the probability that any given student receives an A is 0.10

P(A)=0.1

40% receive a B, This is same as the probability that any given student receives a B is 0.40

P(B)=0.40

and 20% receive a C. This is same as the probability that any given student receives a C is 0.20

P(C)=0.20

The rest would receive other grades (we are not clear what other grades are).

P(Other)=1-(P(A)+P(B)+P(C))=1-(0.1+0.4+0.2)=0.3

We can for the following probability distribution for grades

Grades	Probability
A	0.1
B	0.4
C	0.2
Others	0.3

Next we get the cumulative probability and the random number interval

			Random number interval
Grades	Probability	cumulative probability	From	Less than
A	0.1	0.1	0	0.1
B	0.4	0.5	0.1	0.5
C	0.2	0.7	0.5	0.7
Others	0.3	1	0.7	1

We will multiply by 10 and make the random numbers as integers

			Random number interval	Random number interval (integer values)
Grades	Probability	cumulative probability	From	Less than	From	Less than
A	0.1	0.1	0	0.1	0	1
B	0.4	0.5	0.1	0.5	1	5
C	0.2	0.7	0.5	0.7	5	7
Others	0.3	1	0.7	1	7	10

We can see that the integer values of the ranom number intervals as between 0 to less than 10. Hence we just need 1 digit from the random digit table to simulate 1 trial

Following are the steps to simulate

• Pick a digit from the random digit table
• Note the random number interval in which this digit lies in and pick the corresponding grade.
  • For example, if the random digit is 0,assign A, if it is between 1 and less thn 5 assign B, between 5 and less than 7 assign C and between 7 and less than 10 assign other grades.

ans: b) Assign 1 digit numbers as follows: 0 is A; 1, 2, 3, 4 are B; 5, 6 are C; 7, 8, 9 are other grades.