Question

a student takes an exam containing 7 true or false questions. if a student randomly guesses on the entire exam, what is the standard deviation of the number of incorrect answers? round your answer to two decimal places.

Explanation:

Identify binomial parameters

The number of independent trials is \(n = 7\). Since the student randomly guesses on true or false questions, the probability of getting an incorrect answer on any single question is \(p = 0.5\). The probability of a correct answer is \(q = 1 - p = 0.5\).

Calculate the standard deviation

The standard deviation \(\sigma\) of a binomial distribution is given by:

$$ \sigma = \sqrt{n \cdot p \cdot q} $$

Substituting the values:

$$ \sigma = \sqrt{7 \cdot 0.5 \cdot 0.5} = \sqrt{1.75} \approx 1.3228756 $$

Round to two decimal places

Rounding \(1.3228756\) to two decimal places yields \(1.32\).

Answer:

A student takes an exam containing 7 true or false questions. If a student randomly guesses on the entire exam, what is the standard deviation of the number of incorrect answers? Round your answer to two decimal places. <blank>1.32</blank>