Consumer Banker Association released a report showing the lengths of automobile

Question

Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The results are as follows.

(a) Use the midpoint 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 standard deviation of the distribution. (Round your answers to two decimal places.)

(b) Sketch a graph of the probability distribution for the duration of new auto leases.

Lease Length in Months Percent of Leases 13-24
25-36
37-48
49-60
More than 60 11.5%
38.2%
30.4%
19.6%
0.3% 35 30 25 % of Leases 20 15 10 8.5 30.5 42.5 54.5 66.5 Lease Length in Months

Explanation / Answer

a) Expected lease term , E(X) = 18.5 * 0.115 + 30.5 * 0.382 + 42.5 * 0.304 + 54.5 * 0.196 + 66.5 * 0.003

                                                = 37.58

E(X2) = 18.52 * 0.115 + 30.52 * 0.382 + 42.52 * 0.304 + 54.52 * 0.196 + 66.52 * 0.003 = 1539.25

Var(X) = E(X2) - (E(X))2 = 1539.25 - (37.58)2 = 126.9936

Standard deviation = sqrt(126.9936) = 11.27

b) The correct graph is Option-D)

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