Question

Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Mlinois arrives on time is 0.80. For the questions that follow, consider a sample of twenty randomly selected train trips. 11) (2 points) What is the probability that exactly fifteen trips out of twenty will arrive in Chicago on time? Round to the nearest thousandth. 12) (2 points) What is the probability that at least nineteen trips out of twenty arrive to Chicago on time? Round te the nearest thousandth 13) e points suppose the probability that person does not recycle is 0.23.18 300 randomly selected people were ked Do you recycle would you be surprised is 65 said no to this question? Why?

Answer 1

Hello Sir/ Mam

Given is the case of binomial distribution with,

p	80.00%
n	20

Now, we know that:

P(X =r) = (%) p*(1 – p)a=

Hence,

Q - 11 -

P(X = 15) = (29) 0.815(1 – 0.8) 20-15 = 0.1746

Q - 12 -

P(X > 19 = P(X = 19) + P(X = 20)

P(X > 19) = (20) 0.819(1 – 0.8)20–19 + (20) 0.820(1 – 0.8) 20–20

P(X > 19) = 0.0576 +0.0115 = 0.0692

Thanks!

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