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?Use the normal distribution to approximate the desired probability.

Question
Asked Nov 6, 2019
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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?

Use the normal distribution to approximate the desired probability.

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Expert Answer

Step 1

It is given that P is 0.74 and n is 60.

The number of trains arrived on time x is 38.

Step 2

The required probability is ...

38
-0.74
60
р-Р
P(x35) P
|P(1-Р)
0.74 x (1-0.74)
60
п
=P(z-1.94)
(Using standard normal table
-0.0262
VI
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38 -0.74 60 р-Р P(x35) P |P(1-Р) 0.74 x (1-0.74) 60 п =P(z-1.94) (Using standard normal table -0.0262 VI

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