Question

Ted Olson, director of the company Overnight Delivery, is worried because of the number of letters of first class that his company has lost. These letters are transported in airplanes and trucks, due to that, mister Olson has classified the lost letters during the last two years according to the transport in which the letters were lost. The data is as follows:

Number of cards lost in (month)	J	F	M	A	M	J	J	A	S	O	N	D
Truck	4	5	2	3	2	1	3	5	4	7	0	1
Airplane	5	6	0	2	1	3	4	2	4	7	4	0

Mister Olson will investigate only one department, either aerial o ground department, but not both. He will open the investigation in the department which has the most number of lost letters per month, find:

26.- The expectation quadratic value of lost letters per month for truck.

27.- The expectation quadratic value of lost letters per month for airplane.

28.- The variance value of lost letters per month for truck.

29.- The variance value of lost letters per month for airplane.

Answer 1

(26)

The Expectation value of lost letters per month in truck = Sum of lost letters in truck/12

                                                                                 = (4 +5 + 2 + 3 + 2 + 1+ 3 +5 + 4 + 7 + 0 + 1)/12

                                                                                  = 37/12 = 3.0833

So,

Answer is:

3.0833

(27)

The Expectation value of lost letters per month in airplane = Sum of lost letters in airplane/12

                                                                                 = (5 + 6 + 0+ 2 + 1 + 3 + 4 + 2 + 4 +7 +4 +0)/12

                                                                                  = 38/12 = 3.1667

So,

Answer is:

3.1667

(28)

x	x -	(x - )2
4	0.9167	0.8403
5	1.9167	3.6736
2	- 1.0833	1.1736
3	- 0.0833	0.0069
2	- 1.0833	1.1736
1	- 2.0833	4.3403
3	- 0.0833	0.0069
5	1.9167	3.6736
4	0.9167	0.8403
7	3.9167	15.3403
0	- 3.0833	9.5069
1	- 2.0833	4.3403
Total =		44.9167

Variance value of lost letters per month for truck is given by:

s = 44.9167/11 = 4.0833

So,

Variance value of lost letters per month for truck is 4.0833

(29)

x	x -	(x - )2
5	1.8333	3.3611
6	2.8333	8.0278
0	- 3.1667	10.0278
2	- 1.1667	1.3611
1	- 2.1667	4.6944
3	-0.1667	0.0278
4	0.8333	0.6944
2	- 1.1667	1.3611
4	0.8333	0.6944
7	3.8333	14.6944
4	0.8333	0.6944
0	- 3.1667	10.0278
Total =		55.6667

Variance value of lost letters per month for airplane is given by:

s = 55.6667/11 = 5.0606

So,

Variance value of lost letters per month for airplane is 5.0606