Question

There are 80 questions on an SAT test, and they are all multiple choice with possible answers of a, b, c, d, and e. For each question, only one answer is correct. Find the mean and standard deviation for the numbers of correct answers for those who make random guesses for all 80 questions. Round to one decimal place.

Answer 1

mean = 16

standard deviation= 3.6

Explanation:

As number of questions are 80, consider it 'n' i.e sample size

only one answer is correct from five choices so,

P = 1/5=> 0.2

As we want to find correct answers from the given questions, we will be using binomial distribution for the number of successes (correct answers).

in order to calculate the mean of binomial distribution, take the product of sample size 'n' and probability 'p'

μ=np = 80 x 0.2

μ=16

next to calculate standard deviation, take the square root of the product of sample size 'n' probabilities p and q

where, q= 1-p

σ = sqrt(npq) = sqrt(np(1-p))

σ=
`√(80(0.2)(1-0.2))`

σ= 3.6

the mean is 16 and standard deviation 3.6 for the numbers of correct answers for those who make random guesses for all 80 questions.