Math CentralQuandaries & Queries


Question from Lorie, a student:

4. Merta claims that 74% of its trains are on time.

a. Find the probability that among the 60 trains, 38 or fewer arrived on time.

Hi Lorie,

If you assume that any particular train arriving on time is independent of whether other trains arrive on time (probably an unrealistic assumption) then these are repeated independent trials and hence follow the binomial distribution. If "success" is a train arriving on time then p, the probability of success, is 0.74. You have n = 60 trains and if you let X be the number of them that arrive on time then you want Pr(X ≤ 38).


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