A multiple-choice examination consists of questions, each having possible choice

Question

A multiple-choice examination consists of questions, each having possible choices a, b, c, d, and e. Approximate the probability that a student will get fewer than answers correct if she randomly guesses at each answer. (Note that, if she randomly guesses at each answer, then the probability that she gets any one answer correct is .) Use the normal approximation to the binomial with a correction for continuity. Round your answer to at least three decimal places. Do not round any intermediate steps.

Explanation / Answer

NORMAL APPROXIMATION TO BINOMIAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
mean ( np ) = 20 * 0.2 = 4
standard deviation ( npq )= 20*0.2*0.8 = 1.7889
equation of the normal curve is ( Z )= x - u / sd/sqrt(n) ~ N(0,1)
Assume, no of questions = 20
fewer questions are 6 correct then the probability,

P(X < 6) = (6-4)/1.7889
= 2/1.7889= 1.118
= P ( Z <1.118) From Standard NOrmal Table
= 0.8682

= 0.868

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.