Question

A multiple choice exam has 20 questions. There are four choices for each question. A student guesses the answer to every question. a. Find the chance that the student guesses correctly between four and seven times. (3 points) b. Find the minimum score (number of questions that are correct to get a passing grade) the instructor can set so that the probability that a student will pass just by guessing is 20% or less. (7 points)

Answer 1

Can anyone help answer this question?

Answer 2

The probability of guessing the correct answer to a question is 1/4. Assuming that "between four and seven times" means 4, 5, 6, and 7 times we can use the binomial distribution to find the following probabilities:
\[P(4\ correct)=20C4\times(\frac{1}{4})^{4}\times(\frac{3}{4})^{16}=you\ can\ calculate\]
\[P(5\ correct)=20C5\times(\frac{1}{4})^{5}\times(\frac{3}{4})^{15}=you\ can\ calculate\]
\[P(6\ correct)=20C6\times(\frac{1}{4})^{6}\times(\frac{3}{4})^{14}=you\ can\ calculate\]
\[P(7\ correct)=20C7\times(\frac{1}{4})^{7}\times(\frac{3}{4})^{13}=you\ can\ calculate\]
The required probability for part a is found by adding the above 4 values of probability.

Answer 3

the nCr app on your scientific calculator.