Question

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

Lease Length in Months - Percent of Leases

13-24 15.7%

25-36 37.3%

37-48 25.0%

49-60 21.3%

More than 60 0.7%

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 the two decimal places.)

expected lease term in months:

standard deviation:

Answer 1

The mid point is given by ,

mid point (X) = (Upper class limit + Lower class limit ) / 2

The table given below ,

Lease length in months	Mid points(X)	Percent of Leases P(X)	X*P(X)	X^2*P(X)
13-24	18.5	0.157	2.9045	53.73325
25-36	30.5	0.373	11.3765	346.9833
37-48	42.5	0.25	10.625	451.5625
49-60	54.5	0.213	11.6085	632.6633
More than 60	66.5	0.07	4.655	309.5575
		Sum	41.17	1794.5

Therefore , the expected lease term in months is ,

Now ,

Therefore , the standard deviation is ,