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 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 |

Answer #1

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

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
14.8%
35.8%
28.9%
19.8%
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...

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...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 19 minutes ago

asked 24 minutes ago

asked 26 minutes ago

asked 44 minutes ago

asked 45 minutes ago

asked 47 minutes ago

asked 50 minutes ago

asked 50 minutes ago

asked 53 minutes ago

asked 57 minutes ago

asked 57 minutes ago