A survey of holiday accommodation in New Zealand shows that in Auckland, excluding caravan parks and camping grounds, 42% were full (i.e. had no vacancies). A random sample of 25 holiday accommodation...

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A survey of holiday accommodation in New Zealand shows that in Auckland, excluding caravan parks and camping grounds, 42% were full (i.e. had no vacancies). A random sample of 25 holiday accommodation facilities (of the same capacity) in Auckland is selected at random. Assume the probability that a particular holiday accommodation facility is full is 0.42.

(a) What is the probability that at most 10 of these are full?

(b) What is the probability that no more than

15 of these are full?

Answered 12 days AfterMay 04, 2022

Answer To: A survey of holiday accommodation in New Zealand shows that in Auckland, excluding caravan parks and...

Parvesh answered on May 17 2022

88 Votes

Here, we will use normal approximation to binary distribution.
Here, n=25, p=0.42 and q=1-p=1-0.42=0.58
Mean=np=25*0.42=10.5
sd=sqrt(npq)=sqrt(25*0.42*0.58)=2.47
Let X be random variable showing number of full accommodation facility.
(a) We have to find P(X<=10)
By continuity correction,

...

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A survey of holiday accommodation in New Zealand shows that in Auckland, excluding caravan parks and camping grounds, 42% were full (i.e. had no vacancies). A random sample of 25 holiday accommodation...

Answer To: A survey of holiday accommodation in New Zealand shows that in Auckland, excluding caravan parks and...

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