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ExtremeBDS [4]
3 years ago
9

A multiple choice test has four possible answers for each question. Let X be the number of correct responses in a test of 100 qu

estions if the student simply guesses on each question. The standard deviation of X is
a. 4.33.
b. 18.75.
c. 0.433.
Mathematics
1 answer:
dimulka [17.4K]3 years ago
7 0

Answer:

a. 4.33.

Step-by-step explanation:

If there is only one correct answer out of four alternatives, the expected proportion of correct answers is p =0.25

Sample size (n) = 100 questions

The standard deviation of a proportion 'p' is given by:

s=\sqrt{\frac{p*(1-p)}{n} }

Applying the given data:

s=\sqrt{\frac{0.25*(1-0.25)}{100}}\\s=0.0433

If X is the number of correct responses in 100 guesses, the standard deviation of X is:

\sigma = n*s=100*0.0433\\\sigma = 4.33

The standard deviation of X is 4.33 questions.

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