3-102. A multiple-choice test contains 25 questions, each with four answers. Ass

Question

3-102. A multiple-choice test contains 25 questions, each with four answers. Assume that a student just guesses on each question. (a) What is the probability that the student answers more than 20 questions correctly? (b) What is the probability that the student answers fewer than 5 questions correctly? 3-109. Because all airline passengers do not show up for their reserved seat, an airline sells 125 tickets for a flight that holds only 120 passengers. The probability that a pas- senger does not show up is 0.10, and the passengers behave independently (a) What is the probability that every passenger who shows up ean-take the lighi? (b What is the probability that the flight departs with emp seals?

Explanation / Answer

Solution:-

102)

n = 25

p = 1/4

p = 0.25

a) The probability that the students answer more than 20 questions correctly is 9.6 × 10-10.

x = 20

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x > 20) = 9.6 × 10-10

b) The probability that the students answer fewer than 5 questions correctly is 0.2137.

x = 5

By applying binomial distributiion:-

P(x,n) = nCx*px*(1-p)(n-x)

P(x < 5) = 0.2137

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