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.

(a) Use the Normal approximation to find the probability that Jodi scores 74% or lower on a 100-question test. (Round your answer to four decimal places.)

(b) If the test contains 250 questions, what is the probability that Jodi will score 74% or lower? (Use the normal approximation. Round your answer to four decimal places.)

(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

a) p = 0.8

n = 100

Mean

Standard deviation

Jodi Scores = 74%

The Probability that odi scores 74% or lower on a 100-question test is

b) When n = 250

Mean

Standard Deviation

Jodi Scored = 74%

X = 74% of 250 = 185

c)

Standard deviation is

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

Squaring on both sides

Answer: n = 25