Question

# Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The...

Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The results are as follows. Lease Length in Months Percent of Leases 13-24 25-36 37-48 49-60 More than 60 11.8% 36.4% 25.3% 26.1% 0.4% (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.) expected lease term months standard deviation (b) Sketch a graph of the probability distribution for the duration of new auto leases. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot

Solution:-

a)

 Class interval Percent lease Mid-point 13 to 24 11.80% 18.5 25 to 36 36.40% 30.5 37 to 48 25.30% 42.5 49 to 60 26.10% 54.5 More than 60 0.40% 66.5 Total 100.00%
 Class interval Mid-point (x) Percent lease(P(x) x*P(x) (x - u)^2 P(x)*(x - u)^2 13 to 24 18.5 0.118 2.183 401.1208 47.33225251 25 to 36 30.5 0.364 11.102 64.44878 23.45935738 37 to 48 42.5 0.253 10.7525 15.77678 3.991526352 49 to 60 54.5 0.261 14.2245 255.1048 66.58234862 More than 60 66.5 0.004 0.266 782.4328 3.129731136 Total 1 38.528 1518.884 144.495216

b)