please do ONLY part d, e and f Fall 201 Problem 1. (16 points) The 1200 tenants
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please do ONLY part d, e and f
Fall 201 Problem 1. (16 points) The 1200 tenants of a large apartment building have welght distribution as follon: Weight (pounds) Number of tenants 50 100 150 200 240 300 480 120 Let W be the weight of a tenant in this large apartment building. a. (2 pointa) Find the probability distribution table of W. b. (2 points) what is the expected weight of all tenants, le, -E(W) ? c. (3 points) What is the standard deviation of weight, i.e., = V answer to 3 decimal places) ar W-? (Please round your d. (3 points) In a sample of randomly selected 36 tenants, let W be the avernge weight of the 36 comment on the distribution ofSpecifically, what is the shape of distribution or enants. Please Fall 2017 W? What is E(W)? What is s.e.(W)? (Please round your answer to 3 decimal places.) e. (3 points) Each large elevator in the building has a load limit of 4680 pounds. If 36 tenants crowd into one elevator, what is the probability that this elevator will be overloaded? f. (3 points) Each small elevator in the building has a load limit of 2340 pounds. If 18 tenants crowd into one elevator, what is the probablity that this elevator will be overloaded? If you can not find this probability, please explain why. If you can, please caleulate this probability.Explanation / Answer
a)
W ………50……….100………..150………200
P(W)…… 0.2………0.3………..0.4……….0.1
b)
expected weight = 50 * 0.2 + 100 * 0.3 + 150 * 0.4 + 200 * 0.1
= 120
c)
E(X^2) = 50^2 * 0.2 + 100^2 * 0.3 + 150^2 * 0.4 + 200^2 * 0.1
= 16500
variance = E(X^2) - mean^2
= 16500 - 120^2
= 2100
standard deviation = sqrt(var)
= 10 * sqrt(21) = 45.83
d)
average weight of tenants E(W-bar)= 120
shape of distribution is bell shaped
s.e = 45.83/sqrt(36)
= 7.64
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