Chapter P, Section 4, Exercise 120 Owner-Occupied Housing Units the 2010 US Cens

Question

Chapter P, Section 4, Exercise 120 Owner-Occupied Housing Units the 2010 US Census we learn that 65% of all housing units are owner occupied while the rest are rented. Use this int or at ontofind the follo ng probabilities. (a) If we take a random sample of 20 housing units, find the probability that exactly 15 of them are owner-occupied. Round your answer to four decimal places. the absolute tolerance is +/-0.001 SHOW HINT LINK TO TEXT (b) If we take a random sample of 20 housing units, find the probability that 18 or more of them are owner-occupied. Round your answer to four decimal places. the absolute tolerance is +/-0.003

Explanation / Answer

X ~ Binomial (n,p)

Where n = 20, p = 0.65

The Binomial probability distribution is

P(X) = nCx px ( 1 -p)n-x

a)

P( X = 15) = 20C15 0.6515 0.355

= 0.1272

b)

P( X >= 18) = P( X = 18) + P( X = 19) + P( X = 20)

= 20C18 0.6518 0.352 +20C19 0.6519 0.35 +20C20 0.6520 0.350

= 0.0121

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