   Chapter 8.5, Problem 33E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# In the following problems, use a normal approximation to the binomial.Testing Suppose a final exam contains 120 multiple- choice questions with 5 choices for each answer, and a poorly prepared student knows the answers to 60 questions and guesses on the other 60. What is the probability that she will answer 60% of the questions correctly? More than 60% correctly?

To determine

To calculate: The probability that student will answer 60% question and more than 60% question if there are 120 questions and 5 options for each question.

Explanation

Given Information:

The student knows the 60 answers and other 60 answers she will guess of multiple-choice questions in final exam.

Formula used:

The probability to happen an event is p and for not happen is q,

p=1q

The mean for distribution is np and standard distribution is npq.

The combination formula,

Cnr=n!r!(nr)!

Where n and r are any positive numbers.

Calculation:

Consider the given data.

Total correct questions that she knows are,

n=12060=60

The probability of correct answers out of 5 options,

p=15

q=1p=115=45

Now, mean for the distribution,

np=60(15)=12

And, standard deviation for distribution,

σ=npq=60(15)(45)=9

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