Probability of test questions

Question

find the probability that when a 10 question multiple choice test has 4 possible answers for each question, a student will select at least 6 correct answers from the 10 possible.

Answer 1

10 question test, 4 multiple choice for each question

what is probability a student randomly guessing will get 6 or more right?

use the binomial distribution, as there are only two outcomes, right or wrong.

mean = np = 10(1/4) = 10/4 = 2 1/2 expected correct answers

var = npq = 5/2 x 1/2 = 5/4 = 1 1/4 = Variance

sd = sqrnpq = sqr(5/4) = (sqr5)/2 = about 2.2/2 = about 1.1 = standard deviation

z score for 6 = ((x -xbar)/sd = (6- 2.5)/1.1 = 3.5/1.1 = about 3.18

use z tables or a z calculator to find area under the curve for z=3.8 to z = infinity

Pr(6+ correct) = about .0.00007 = about .007% chance

= less than 1/100th of 1% chance

= 0 % chance if rounded to 1 decimal place