Problem 1. (16 points) The 1200 tenants of a large apartment building have weigh

Question

Problem 1. (16 points) The 1200 tenants of a large apartment building have weight distribution as follow: Weight (pounds) Number of tenants 50 100 150 240 360 480 200 120 Let W be the weight of a tenant in this large apartment building. a (2 points) Find the probability distribution table of w b. (2 points) what is the expected weight of all tenants, ie, = E(W) =? (3 points) what is the standard deviation of weight, ie, = VVar W-? (Please round your answer to 3 decimal places.) d. (3 points) In a sample of randomly selected 36 tenants, let W be the average weight of the 36 tenants. Please comment on the distribution of W. Specifically, what is the shape of distribution of

Explanation / Answer

a.

b)

E(X) = 120

c)

std. dev. = sqrt(2100) = 45.8258

d)

Shape of the distribution would be approximately normal i.e. bell curved.
E(W) = 120
s.e.(W) = 45.8258/sqrt(36) = 7.638

Weight Number of tenants P(X) 50 240 0.2 100 360 0.3 150 480 0.4 200 120 0.1 1200

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