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 12.7%
25-36 37.1%
37-48 28.5%
49 - 60 21.5%
More than 60 0.2%

(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.

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

Answer 1

To find the expected lease term and standard deviation, midpoints of the lease lengths and their corresponding percentages are used. A graph is then sketched to illustrate the probability distribution of these automobile lease lengths.

Step-by-step explanation:

The student's question requires us to calculate the expected lease term and standard deviation for automobile leases, and then to sketch a graph of the probability distribution for said leases. To calculate the expected value or mean lease term, we use the midpoint of each lease length class and the corresponding percentage of leases. Using the last class midpoint of 66.5 months helps to find a value in line with the given percentages. After calculating the mean, we then apply the formula for standard deviation to find the spread of the lease lengths around the mean.

To sketch the graph of the probability distribution for the duration of new auto leases, we would plot the midpoints of the lease length intervals on the x-axis and plot the corresponding percentages on the y-axis, resulting in a histogram reflecting the distribution of lease lengths.