Question

When taking a 11 question multiple choice test, where each question has 4 possible answers, it would be unusual to get 3 Incorrect or more questions correct by guessing alone. Note: Of course it would be unusual to get 11 questions correct. You need to enter the smallest possible number of questions to make getting "that many correct" unusual.

Answer 1

6

Explanation:

probability of answering a question correct p=1/4

let minimum number number of question that would be unusual =n

hence from binomial distribution P(X>=n) <0.05

`\sum_(x=n)^(11)\binom{11}{x}(1/4)^(x)(3/4)^(11-x) <0.05`

by solving:

n=6

it would be unusual to get 6 or more questions correct by guessing alone.