Question
Asked Nov 9, 2019
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A hotel manager calculates that 12% of the hotel rooms are booked.

If the manager is right, what is the probability that the proportion of rooms booked in a sample of 556 rooms would be less than 10%? Round your answer to four decimal places.

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Expert Answer

Step 1

From the given information,

P be the probability that hotel rooms are booked = 0.12.

Sample size (n) =556,

By normal approximation of binomial,

Thus,

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p 0.12 q 1p =0.88 =556x 0.12 =66.72 рg п 0.12x 0.88 556 0.013

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Step 2

So, probability that the proportion of rooms booked in a sample...

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0.10- P(p<0.10) PZ<- 0.10-0.12 = PZ < 0.12 x0.88 556 0.02 = P Z<- 0.013 P(Z <-1.53) = 0.063

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Statistics

Advanced Topics in Statistics

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