Question

A multiple-choice test has 6 questions. There are 4 choices for each question. A student who has not studied for the test decides to answer all questions randomly with a Probability of success = p =.25. Let X represent the number of correct answers out of six questions.

(i) Use binomial distribution to complete the table

(ii) Find the probability that the student will be successful in at least 4 questions.

(iii) Find the probability that the student will be successful in at most 3 problems

(iv) Compute the mean μ and the standard deviation σ for this problem.

X	P(x)

Answer 1

1)

This is a binomial distribution question with

n = 6

p = 0.25

q = 1 - p = 0.75

where

2)b)

3)

x = 3

4)

Since we know that

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