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fomenos
3 years ago
9

The director of the library believes that 14% of the library's collection is checked out. If the director is right, what is the

probability that the proportion of books checked out in a sample of 478 books would be less than 13%? Round your answer to four decimal places.
Mathematics
1 answer:
Ksivusya [100]3 years ago
5 0

Answer: 0.2643

Step-by-step explanation:

Let p be the population proportion and \hat{p} be the sample proportion .

As per given question , we have

p=0.14\\\\ \hat{p}=0.13\\\\ n=478

z-score : \dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}

z=\dfrac{0.13-0.14}{\sqrt{\dfrac{0.14(1-0.14)}{478}}}\\\\=-0.630087269176\approx-0.63

The required probability ( using z-table ):-

P(z

Hence, the probability that the proportion of books checked out in a sample of 478 books would be less than 13% = 0.2643

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