A multiple choice quiz has ten questions, each with four answer choices where on

Question

A multiple choice quiz has ten questions, each with four answer choices where only one answer is correct. A student hasn't studied at all and decides to guess the answer to randomly. a) What is the probability the student answers exactly 2 of the 10 questions correctly? b) What is the probability the student answers more than 2 of the 10 questions correctly? c) What is the probability the student answers 5 or fewer of the 10 questions correctly? A factory produces stand-up desks for offices. It has been determined that 0.1% of the desks have an issue with the motor that requires an extra adjustment before shipment. In a sample of 1, 200 desks, what is the probability that 2 or fewer will have this issue?

Explanation / Answer

Solution:

4 a) What is the probability the student answers exactly 2 of the 10 questions correctly
binompdf(10, 1/4, 2) = 0.2815
b) What is the probability the student answers more than 2 of the 10 questions correctly
P(X > 7) = P(X = 1)+ P(X = 2)+ P(X = 3) + P(X = 4)+ P(X = 5) + P(X = 6) = P(X = 7)+ P(X = 8) +P(X=9)+P(X=10)
= 0.1877+ 0.2815+ 0.2502+ 0.1459+ 0.0583+ 0.0162+ 0.0030+ 0.0003+ 0+ 0
= 0.9431
c) What is the probability the student answers 5 or fewer of the 10 questions correctly
binomcdf(10, 1/4, 5) = 0.0197

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