Final answer:
Using the Range Rule of Thumb for Unusual Values, it would be unusual to guess more than 8 questions correctly on a 23 question multiple choice test with five possible answers each.
Step-by-step explanation:
To determine how unusual it is to get a certain number of questions correct by guessing on a multiple choice test, we can use the Range Rule of Thumb for Unusual Values. Given a 23-question test with five possible answers each, the expected number of correct answers by guessing alone is the product of the number of questions and the probability of guessing a question correctly, which is 1/5.
The expected number of correct answers is 23 * (1/5), which equals 4.6. To find the Range Rule of Thumb for Unusual Values, we calculate the standard deviation of a binomial distribution.
The standard deviation, σ, for a binomial distribution is calculated with the formula σ = √(np(1-p)), where n is the number of trials (23 questions), and p is the probability of success (1/5).
Plugging in the values, we get σ = √(23*(1/5)*(4/5)) = √(3.68) ≈ 1.92.
The Range Rule of Thumb states that values outside the range of (mean - 2*standard deviation, mean + 2*standard deviation) are considered unusual. Therefore, to find the range of usual values, we calculate:
- Lower bound = Mean - 2*Standard Deviation = 4.6 - 2*1.92 = 0.76
- Upper bound = Mean + 2*Standard Deviation = 4.6 + 2*1.92 = 8.44
Since we're interested in whole numbers of questions, we consider values outside the range of 1 to 8 as unusual.
To answer the initial question, it would be unusual for a student to guess more than 8 questions correctly on a 23 question test with 5 possible answers each.