Question

John is going to take a quiz with 10 multiple choices questions. Each question has only one correct answer out of 4 choices. Suppose John simply answers each question by random guess,
(a) What is the probability of getting 5 questions answered correctly?
(b) What is the expected number and standard deviation of the number of correctly
answered questions?

Answer 1

(a)

Binomial Distribution

n = 10

p = 0.25

q = 1 - p = 0.75

So,

Answer is:

0.0584

(b)

(i)

mean = np = 10 X 0.25 = 2.5

So,

Answer is:

2.5

(ii)

Standard Deviattion =

So,

Answer is:

1.3693