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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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Answers:

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===========================================

Explanation:

Divide the second term over the first to get 30/20 = 1.5

Divide the third term over the second term to get 45/30 = 1.5

The common ratio is 1.5, which means we multiply 1.5 by each term to get the next term

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fourth term = 1.5*(third term) = 1.5*45 = 67.5

fifth term = 1.5*(fourth term) = 1.5*67.5 = 101.25

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As a shortcut you can plug n = 4 and n = 5 into the function t(n) = 20*(1.5)^(n-1) to get the fourth and fifth terms respectively.

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