Merta reports that 74% of its trains are on time. A check of 60 randomly selected trains shows that 38 of them arrived on time. Find the probability that among the 60 trains, 38 or fewer arrive on time. Based on the result, does it seem plausible that the "on-time" rate of 74% could be correct?
A).0409 , yes
B).0316 , yes
C).0316 , no
D).0409 , no

Question

Quizplus · Accepted Answer

Using the binomial distribution or a normal approximation to the binomial distribution, we can calculate the probability of 38 or fewer trains arriving on time out of 60, given a success rate of 74%. The calculation yields a probability of approximately .0409. This probability, while low, is not so extreme as to definitively rule out the possibility that the true on-time rate is 74%. Therefore, it's plausible, though perhaps somewhat unlikely, that the "on-time" rate of 74% could be correct.

Merta Reports That 74% of Its Trains Are on Time