Question 271871: Use the normal distribution to approximate the desired probability. International Airlines reports that 74% of its planes are on time. A check of 60 randomly selected planes shows that 38 of them arrived on time. Find the probability that among the 60 planes, 38 or fewer arrive on time.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Use the normal distribution to approximate the desired probability. International Airlines reports that 74% of its planes are on time.
A check of 60 randomly selected planes shows that 38 of them arrived on time. Find the probability that among the 60 planes, 38 or fewer arrive on time.
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If p = 0.74, the mean for all samples of size 60 is np = 60*0.74 = 44.4
and the standard deviation is sqrt(npq) = sqrt(60*0.74*0.26) = 3.3976
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Then z(38) = (38-44.4)/3.3976 = -1.8837
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P(x<=38) = P(z< -1.8837) = 0.0298
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Cheers,
Stan H.
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