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Chapter 5: Q2 (page 220)

There are 80 questions from an SAT test, and they are allmultiple choice with possible answersof a, b, c, d, e. For each question, only one answer is correct. Find the mean and standarddeviation for the numbers of correct answers for those who make random guesses for all 80

questions.

Short Answer

Expert verified

The mean value is 16.

The standard deviation is 3.6.

Step by step solution

01

Given information

The number of questions from a SAT test is n=80.

The possible number of choices for an answer is a,b,c,d,e.

02

Compute the mean 

Let x represents the number of correct answers for those who make random guesses.

The probability of selecting a correct answer is p=15.

The mean value is computed as,

μ=np=80×15=16

Therefore, the mean value of the number of correct answers for those who make random guesses for all 80 questions is 16.

03

Compute the standard deviation 

The standard deviation is computed as,

σ=npq=80×15×45=3.577≈3.6

Thus, the standard deviation of the number of correct answers for those who make random guesses for all 80 questions is 3.6.

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