Question

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 = 0.82. Use 4 decimal places.

(a) Use the normal approximation to find the probability that Jodi scores 77% or lower on a 100-question test.

(b) If the test contains 250 questions, what is the probability that Jodi will score 77% or lower?

Answer 1

Q) Given that, p = 0.82

We want to find, the following probabilities,

a) n = 100, p-hat = 0.77

The probability is 0.0968

b) n = 250, p-hat = 0.77

The probability is 0.0197