A choice answer exam (4 choices per question) has 10 questions. A student who has not studied at all randomly answers all questions independently. a) What grade can he expect? With what standard deviation? b) What is the probability that he has exactly 7 correct answers? c) What is the probability that he obtains at least 60% on this exam?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A choice answer exam (4 choices per question) has 10 questions. A student who has not studied at all
randomly answers all questions independently.
a) What grade can he expect? With what standard deviation?
b) What is the probability that he has exactly 7 correct answers?
c) What is the probability that he obtains at least 60% on this exam?
d) What is the probability that he gets at least one correct answer?

Expert Solution
Step 1: introduction

Given 

 n = 10 (number of questions), k = 7 (number of correct answers), and p = 1/4 (probability of a correct answer). 

Binomial distribution formula

P(X=k)=(n choose k)*pk*(1-p)(n-k)

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