Question

Consider taking a multiple choice exam with 25 questions and 5 possible answers per question. Assuming you randomly guess, let Y = number of questions out of the 25 you get wrong.

a. What is the distribution TYPE for Y? Be sure to give values for its parameters.
b. Give the functional form of the pmf for Y.
c. In tabular form, write out the pmf of Y.
d. Give the histogram for the pmf of Y.
e. Find the mean of Y.
f. Find the standard deviation of Y.

Answer 1

a)Y follows binomial distribution with parameter n=25 and p=probability of getting a question wrong =4/5

b)

P(Y=y)=(₂₅C_y)*(4/5)^y(1/5)^25-y

c)

y	P(y)
0	0.0000
1	0.0000
2	0.0000
3	0.0000
4	0.0000
5	0.0000
6	0.0000
7	0.0000
8	0.0000
9	0.0000
10	0.0000
11	0.0001
12	0.0003
13	0.0012
14	0.0040
15	0.0118
16	0.0294
17	0.0623
18	0.1108
19	0.1633
20	0.1960
21	0.1867
22	0.1358
23	0.0708
24	0.0236
25	0.0038

d)

e)

mean =np=25*4/5 =20

f)

standard deviation =sqrt(np(1-p)) =sqrt(25*4/5*(1-4/5))=2