# Bedrooms #Houses 4 3783 The American Housing Survey reported the following dat

Question

# Bedrooms #Houses

4 3783

The American Housing Survey reported the following data on the number of bedrooms in renter occupied houses in central cities .

# Bedrooms #Houses

0 23 1 541 2 3832 3 8690

4 3783

Determine the expected number of bedrooms in renter occupied houses. (3 points) What is the standard deviation of the number of bedrooms (3 points) What is the probability that the number of bedrooms will be less than the expected number of bedrooms? (2 points) What is the probably that a renter occupied house has 3 or more bedrooms? (2 points)

Explanation / Answer

P(X = 0 ) = 23/16869 = 0.001

P(X = 1) = 541/16869 = 0.032

P(X = 2) = 3832/16869= 0.227

P(X = 3) = 8690/16869 = 0.515

P(X = 4) = 3783/16869 = 0.224

A) Expected value(E(x)) = 0 * 0.001 + 1 * 0.032 + 2 * 0.227 + 3 * 0.515 + 4 * 0.224 = 2.927

B) (E(x2)) = 0^2 * 0.001 + 1^2 * 0.032 + 2^2 * 0.227 + 3^2 * 0.515 + 4^2 * 0.224 = 9.159

variance = (E(X2)) - (E(X))2

              = 9.159 - (2.927)^2 = 0.592

Standard deviation = sqrt(0.592) = 0.769

c) Probability = P(x = 0) + P(x = 1) + P(x = 2)

                      = 0.001 + 0.032 + 0.227 = 0.26

d) Probability = P(x = 3) + P(x = 4)

                      = 0.515 + 0.224 = 0.739

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