SOLUTION: If 20% of the residents in Washington prefer a white telephone over any other color available, what is the probability that among the next 1000 telephone installed in the city i)

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Question 98165: If 20% of the residents in Washington prefer a white telephone over any other color available,
what is the probability that among the next 1000 telephone installed in the city
i) between 170 and 185 inclusive will be white
ii) at least 210 but not more than 225 will be white
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
If 20% of the residents in Washington prefer a white telephone over any other color available,
what is the probability that among the next 1000 telephone installed in the city
i) between 170 and 185 inclusive will be white
It's a binomial problem that requires a normal approximation answer.
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With p=0.20 and n=1000, mean=np = 200; std. dev. = sqrt(npq)=sqrt(160) = 4sqrt10
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Find the z-score of 170 and the z-score of 185
Find the area under the normal curve over the interval between those two z-values
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ii) at least 210 but not more than 225 will be white
Find the z score for 210 and for 225
Find the area between those two z scores
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Cheers,
Stan H.