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 15.4% 36.4% 25.6% 21.9% 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 standard deviation

Solution:

The formula for mean and standard deviation for the probability distribution is given as below:

Mean = ∑XP(X)

Variance = ∑ P(X)*(X - mean)^2

SD = sqrt[∑ P(X)*(X - mean)^2]

The calculation table is given as below:

 Class Midpoint X P(X) XP(X) (X - Mean)^2 P(X)*(X - mean)^2 13 to 24 18.5 0.154 2.849 350.887824 54.0367249 25 to 36 30.5 0.364 11.102 45.319824 16.49641594 37 to 48 42.5 0.256 10.88 27.751824 7.104466944 49 to 60 54.5 0.219 11.9355 298.183824 65.30225746 More than 60 66.5 0.007 0.4655 856.615824 5.996310768 Total 1 37.232 148.936176

From above table, we have

Mean = ∑XP(X) = 37.232

Expected lease term = Mean = 37.232

Variance = ∑ P(X)*(X - mean)^2

Variance = 148.936176

SD = sqrt(148.936176)

Standard deviation = 12.203941

#### Earn Coins

Coins can be redeemed for fabulous gifts.