Question

Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.8.

Use 4 decimal places.



(a) Use the normal approximation to find the probability that Jodi scores 75% or lower on a 100-question test.

(b) If the test contains 250 questions, what is the probability that Jodi will score 75% or lower?

(c) How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?

Answer 1

Q) Given that, p = 0.8

We want to find, the following probabilities,

a) n = 100, p-hat = 0.75

The probability is 0.1056

b) n = 250, p-hat = 0.75

The probability is 0.0239

c) We want to find, n such that, standard deviation of Jodi's proportion of correct answers to half its value for a 100-itrm test.

We want to find new n such that,

Answer: n = 400