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 12.7% 35.5% 30.7% 20.9% 0.2% 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

First we will find the mid points

Mid point for class 13-24 = (13+24)/2 = 18.5

Similarly we will compute for others

Mid points(x). P(x)

18.5. 0.127

30.5. 0.355

42.5. 0.307

54.5. 0.209

66.5. 0.002

Expected value is given by sum of x*p(x)

= 18.5*0.127 + 30.5*0.355 +........

= 37.748

To find the standard deviation

First we need to subtract mean from each and every observation and then take the square and then multiply them with their respective probabilities and then add them and take the square root of the end result

=√{ (18.5-37.748)^2*0.127 + (30.5-37.748)^2*0.355...}

= 11.5299

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