Question

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	12.7% 38.8% 27.7% 20.1% 0.7%

(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.

Answer 1

a)

X=mid point	P(X)	X*P(X)	X² * P(X)
18.5	0.1270	2.350	43.466
30.5	0.3880	11.834	360.937
42.5	0.2770	11.773	500.3313
54.5	0.2010	10.9545	597.0203
66.5	0.007	0.4655	30.9558

	P(X)	X*P(X)	X² * P(X)
total sum =	1	37.376	1532.71

expetced lease term = mean = E[X] = Σx*P(X) =            37.37600
          
E [ X² ] = ΣX² * P(X) =            1532.7100
          
variance = E[ X² ] - (E[ X ])² =            135.7446
          
std dev = √(variance) =            11.65

b)