# Normal distribution to approximate the desired probability

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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?

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The solution examines normal distributions to approximate the desired probability. Based on the results, the expert determines if it is plausible that the on time rate of 74% could be correct.

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The binomial distribution with the parameters p= 0.74 and n =60

Then np = 44.4 and n (1-p) = 15.6 and therefore we can apply normal approximation to binomial ...

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