Question

A multiple-choice test consists of 20 items, each with four choices. A student is able to...

A multiple-choice test consists of 20 items, each with four choices. A student is able to eliminate one of the choices on each question as incorrect and chooses randomly from the remaining three choices. A passing grade is 12 items or more correct. Let X be the number of questions the student answers correctly.

a) What is the pdf of X?

b) What is the probability that the student passes?

c)What is the E(X) & Var(X)?

d)What is the m.g.f of X?

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Solution: The given process (number of questions the student answers correctly) follows the binomial distribution with n=20 and probability of succes .

a) What is the pdf of X?

Answer: Since X follows Binomial distribution, therefore the pdf of X is given below:

b) What is the probability that the student passes?

Answer: A student passes if he/she answers 12 or more correct. Therefore the probability that the student passes is

  

Therefore the probability that the student passes is 0.01297

c)What is the E(X) & Var(X)?

Answer:

  

d)What is the m.g.f of X?

Answer: The m.g.f of binomial distribution is given below:

Therefore the m.g.f is

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