Lease Length in Months Percent of Leases 13-24 25-36 37-48 49-60 More than 60 13

Question

Lease Length in Months Percent of Leases 13-24 25-36 37-48 49-60 More than 60 13.0% 33.8% 29.8% 17.8% 0.6% (a) Use the midpcint of each class, and call the midpoint of the last class 66.5 months, for purposes of computing the expected lease term. Also find the standaro deviation of the distribution. (Round your answers to two decimal places.) expected lease tern standard deviaticn months (b) Sketch a graph of the probability distribution for the duration of new auto leases 30 of Leases 20 10 30 efLesses ho

Explanation / Answer

a) E(X) = 18.5 * 0.13 + 30.5 * 0.388 + 42.5 * 0.298 + 54.5 * 0.178 + 66.5 * 0.006 = 37.004 = 37 months

E(X2) = 18.52 * 0.13 + 30.52 * 0.388 + 42.52 * 0.298 + 54.52 * 0.178 + 66.52 * 0.006 = 1499.44

Var(X) = E(X) - (E(X)) = 1499.44 - 372 = 130.44

Standard deviation = sqrt(130.44) = 11.42 months

b) Option-A)

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