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 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:

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 ,

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