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iris [78.8K]
3 years ago
14

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?
Mathematics
1 answer:
kenny6666 [7]3 years ago
6 0

Answer:

No, the on-time rate of 74% is not correct.

Solution:

As per the question:

Sample size, n = 60

The proportion of the population, P' = 74% = 0.74

q' = 1 - 0.74 = 0.26

We need to find the probability that out of 60 trains, 38 or lesser trains arrive on time.

Now,

The proportion of the given sample, p = \frac{38}{60} = 0.634

Therefore, the probability is given by:

P(p\leq 0.634) = [\frac{p - P'}{\sqrt{\frac{P'q'}{n}}}]\leq [\frac{0.634 - 0.74}{\sqrt{\frac{0.74\times 0.26}{60}}}]

P(p\leq 0.634) = P[z\leq -1.87188]

P(p\leq 0.634) = P[z\leq -1.87] = 0.0298

Therefore, Probability of the 38 or lesser trains out of 60 trains to be on time is 0.0298 or 2.98 %

Thus the on-time rate of 74% is incorrect.

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4 0
3 years ago
Find of the areas of the squares PQRSto that of ABCD where PQ=9cm and AB=5cm​
Ket [755]

Answer: Area of square PQRS is 81cm^2 and of ABCD is 25cm^2

You know its a square. Which means all the sides are equal and same length. If you dont know what's a square then here is the definition:

Square is a plane figure with four equal sides and four right (90°) angles.

So now we know both of are squares, in case of the first square, PQRS, one side length is already given which is PQ=9cm. Now one side is 9cm which means all the sides are 9cm's (PQ=9cm, QR=9cm, RS=9cm,SP=9cm). So to find area just multiply them:

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Now you found the area of the first square. So for the second square, ABCD, one side length is 5 cm so all the rest three sides are also 5 cm. Again, multiply them in order to find the area:

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CAUTIONS: IT IS NOT THAT HARD YA KNOW

By the way, hope it helps! ^^

7 0
2 years ago
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