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The director of the library believes that 13% 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 774 books would be less than 10%

User Sequielo
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1 Answer

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Answer:

The probability that the proportion of books checked out in a sample of 774 books would be less than 10% is 0.0066

Explanation:

We are given that The director of the library believes that 13% of the library's collection is checked out.


\mu = p = 0.13

Total no. of books = 774

Standard deviation =
\sqrt{(p(1-p))/(n)}

Standard deviation =
\sqrt{(0.13(1-0.13))/(774)}=0.012

We are supposed to find the probability that the proportion of books checked out in a sample of 774 books would be less than 10%


P(\hat{p}<0.1)\\Z=(x-\mu)/(\sigma)\\Z=(0.1-0.13)/(0.012)\\Z=-2.48\\P(Z<-2.48)=0.0066

So,
P(\hat{p}<0.1)=0.0066

Hence the probability that the proportion of books checked out in a sample of 774 books would be less than 10% is 0.0066

User Salman Hasrat Khan
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