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Ivenika [448]
3 years ago
12

The director of the library calculates that 29% of the library's collection is checked out. If the director is right, what is th

e probability that the proportion of books checked out in a sample of 412 books would differ from the population proportion by less than 4%? Round your answer to four decimal places.
Mathematics
1 answer:
marusya05 [52]3 years ago
8 0

Answer:

The probability that the proportion of books checked out in a sample of 412 books would differ from the population proportion by less than 4% is P=0.9255.

Step-by-step explanation:

The population's proportion is \pi=0.29

If we take a sample of 412 books (n=412), we have a standard deviation of the sampling distribution of:

\sigma_M=\sqrt{\frac{\pi(1-\pi)}{n}}=\sqrt{\frac{0.29*0.71}{412}}=\sqrt{0.0005} =0.0224

We have to calculate the probabilty that the sample proportion will be between 0.25 and 0.33.

z_1=(0.25-0.29)/0.0224=-0.04/0.0224=-1.7857\\\\z_2=1.7857\\\\\\P(0.25

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