Question 11 (5 points) The probability that a randomly selected commuter listens

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Question 11 (5 points) The probability that a randomly selected commuter listens to audiobooks during their commute is 0.37. Suppose that a sample of 11 commuters is selected, what is the probability that at most 3 of them listen to audiobooks? Write only a number as your answer. Round to 2 decimal places (for example 0.24). Do not write as a percentage. Your Answer: Answer Save Question 12 (5 points) At a car rental agency, 0.33 of the cars are returned on time. A sample of 12 car rentals is studied. What is the probability that more than 3 of them are returned on time? Write only a number as your answer. Round to 2 decimal places (for example 0.24). Do not write as a percentage. Your Answer:

Explanation / Answer

Question 11)

X ~ Binomial (n,p)

Where n = 11 , p = 0.37

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

Therefore,

P( X <= 3) = P( X = 0) + P( X = 1) + P( X = 2) + P( X = 3)

= 11C0 0.370 0.6311 +11C1 0.371 0.6310 +11C2 0.372 0.639 +11C3 0.373 0.638

= 0.3714

P(X <= 3) = 0.37 (Rounded to 2 decimal places)

Question 12)

X ~ Binomial (n,p)

Where n = 12 , p = 0.33

Binomial probability distribution is

P(X) = nCx px (1-p)n-x

So,

P( X > 3) = 1 - P( X <= 3)

= 1 - [ P( X = 0) + P( X = 1) + P( X = 2) + P( X = 3) ]

= 1 - [ 12C0 0.330 0.6712 +12C1 0.331 0.6711 +12C2 0.332 0.6710 +12C3 0.333 0.679 ]

= 1 - 0.4027

= 0.5973

P( X > 3) = 0.60 (Rounded to 2 decimal places)

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