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 = 0.76.

(a) Use the Normal approximation to find the probability that Jodi scores 72% 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 72% or lower? (Use the normal approximation. Round your answer to four decimal places.)

Answer 1

Answer)

We need to use standard normal z table to solve the problem

N = 100

Po = 0.76

P = 0.72

Z = (P-Po)/standard error

Standard error = √{po*(1-po)}/√n

After substitution

Z = -0.94

From z table, P(z<-0.94) = 0.1736

B)

Here n = 250

So, z = -1.48

From z table, P(z<-1.48) = 0.0694