Question

Customer	Type of Customer	Items	Net Sales	Method of Payment	Gender	Marital Status	Age
1	Regular	1	49.5	Discover	Male	Married	22
2	Promotional	1	112.4	Proprietary Card	Female	Married	26
3	Regular	1	32.5	Proprietary Card	Female	Married	22
4	Promotional	5	110.4	Proprietary Card	Female	Married	18
5	Regular	2	64	MasterCard	Female	Married	24
6	Regular	1	54.5	MasterCard	Female	Married	34
7	Promotional	2	88	Proprietary Card	Female	Married	20
8	Regular	1	32.5	Visa	Female	Married	30
9	Promotional	2	66.52	Proprietary Card	Female	Married	36
10	Regular	1	54.5	Proprietary Card	Female	Married	26
11	Regular	1	39.5	Proprietary Card	Female	Married	38
12	Promotional	1	41.6	Proprietary Card	Female	Married	30
13	Promotional	9	170.4	Visa	Female	Married	30
14	Promotional	2	74.5	Visa	Female	Married	36
15	Regular	1	59.5	Visa	Male	Single	44
16	Promotional	2	81.4	Proprietary Card	Male	Single	26
17	Promotional	3	104	Proprietary Card	Female	Single	32
18	Regular	3	64.5	Discover	Female	Married	30
19	Promotional	2	48.5	MasterCard	Female	Married	22
20	Promotional	6	54.8	Proprietary Card	Female	Married	46
21	Promotional	1	41.6	Proprietary Card	Female	Single	18
22	Promotional	4	80.82	Proprietary Card	Female	Married	28
23	Promotional	7	276	American Express	Female	Married	40
24	Regular	2	84	Proprietary Card	Female	Married	32
25	Promotional	2	49.5	Visa	Male	Married	38
26	Promotional	1	40.02	Proprietary Card	Female	Married	50
27	Regular	1	54.5	Proprietary Card	Female	Married	44
28	Promotional	5	202.8	Proprietary Card	Female	Single	32
29	Promotional	3	81.2	Proprietary Card	Female	Married	22
30	Promotional	1	28	Proprietary Card	Female	Married	60
31	Promotional	2	73.2	MasterCard	Female	Married	18
32	Regular	1	85	Proprietary Card	Female	Married	42
33	Promotional	3	73.2	Proprietary Card	Female	Married	34
34	Regular	1	50	Proprietary Card	Female	Married	24
35	Promotional	5	115.5	MasterCard	Female	Married	46
36	Regular	1	39.5	MasterCard	Male	Single	26
37	Regular	2	112.5	Visa	Female	Single	32
38	Promotional	6	127.5	Proprietary Card	Female	Married	40
39	Promotional	5	23.23	Proprietary Card	Female	Married	34
40	Regular	2	62.5	Proprietary Card	Female	Married	48
41	Promotional	13	208.8	Proprietary Card	Female	Married	32
42	Promotional	4	29.5	Visa	Female	Married	36
43	Regular	2	133.5	Proprietary Card	Female	Married	38
44	Promotional	1	72.4	Proprietary Card	Female	Married	44
45	Promotional	2	33.8	Proprietary Card	Female	Married	28
46	Promotional	2	49.6	Proprietary Card	Female	Married	50
47	Regular	1	35	MasterCard	Female	Married	36
48	Promotional	3	73.64	Proprietary Card	Female	Married	20
49	Promotional	1	24.82	Proprietary Card	Female	Married	22
50	Promotional	9	155.2	MasterCard	Female	Married	36
51	Promotional	6	186.62	Proprietary Card	Female	Married	28
52	Promotional	5	128.8	Proprietary Card	Male	Married	58
53	Regular	1	68	Discover	Female	Single	68
54	Regular	2	84	Visa	Female	Single	84
55	Regular	2	59.5	MasterCard	Female	Married	22
56	Promotional	3	151.6	Proprietary Card	Female	Married	28
57	Promotional	6	133.1	Proprietary Card	Female	Married	44
58	Promotional	2	90.4	Proprietary Card	Female	Married	38
59	Promotional	4	75.2	MasterCard	Female	Married	36
60	Promotional	4	123	Proprietary Card	Female	Single	40
61	Promotional	1	118.8	Proprietary Card	Female	Married	36
62	Promotional	3	69.91	Proprietary Card	Female	Single	20
63	Promotional	5	63.6	Proprietary Card	Female	Married	44
64	Promotional	1	41.6	Proprietary Card	Female	Single	32
65	Promotional	2	59.5	Proprietary Card	Female	Married	38
66	Promotional	1	49.6	Proprietary Card	Female	Married	52
67	Promotional	2	69.5	Proprietary Card	Female	Married	24
68	Promotional	5	156.8	Proprietary Card	Female	Married	18
69	Promotional	2	57.2	Proprietary Card	Male	Married	36
70	Promotional	8	105.05	Proprietary Card	Female	Married	44
71	Promotional	5	165.32	Proprietary Card	Female	Married	20
72	Promotional	4	68	MasterCard	Female	Married	22
73	Regular	1	79	Proprietary Card	Female	Single	54
74	Promotional	2	56.5	Proprietary Card	Female	Married	22
75	Promotional	2	55.22	Proprietary Card	Female	Married	64
76	Promotional	4	94.74	Proprietary Card	Female	Married	52
77	Regular	2	49	Proprietary Card	Female	Married	32
78	Promotional	4	121.14	Proprietary Card	Female	Married	18
79	Promotional	3	96.8	Proprietary Card	Female	Married	28
80	Regular	2	99	Discover	Female	Married	44
81	Promotional	2	88	MasterCard	Female	Married	58
82	Promotional	6	63.2	Proprietary Card	Female	Single	20
83	Promotional	4	68.5	Visa	Female	Married	26
84	Promotional	3	56	Proprietary Card	Female	Married	34
85	Regular	2	47.5	Visa	Female	Married	34
86	Promotional	1	30.8	Proprietary Card	Female	Married	52
87	Regular	6	154	MasterCard	Female	Single	38
88	Regular	4	117	Proprietary Card	Female	Married	26
89	Promotional	1	41.6	Proprietary Card	Female	Single	50
90	Promotional	6	67.6	Proprietary Card	Female	Married	32
91	Promotional	4	105.2	Proprietary Card	Female	Married	44
92	Promotional	1	32.42	Proprietary Card	Female	Married	44
93	Regular	5	169.75	Proprietary Card	Female	Married	62
94	Promotional	17	239.5	Proprietary Card	Female	Married	20
95	Regular	3	76	American Express	Female	Married	36
96	Regular	1	49.5	MasterCard	Female	Married	34
97	Promotional	9	263	Proprietary Card	Female	Married	20
98	Promotional	10	297.59	Proprietary Card	Female	Married	42
99	Promotional	2	57.6	Proprietary Card	Female	Married	20
100	Promotional	1	38.44	Proprietary Card	Female	Married	34

a) Using the empirical rule, 95% of female promotional customer ages should be between what two values? Either show work or explain how your answer was calculated.

b)Using the empirical rule, 68% of items purchased should be between what two values? Either show work or explain how your answer was calculated.    

Answer 1

We can use the excel to filter the given data set .

First copy the given data set into the excel , then select all the data set go to "Data" menu --> click on "Filter" . Then click the filter symbol at "Types of the customers " Check the box for promotions and similarly click the filter symbol at "Gender" and check the box for female.

You will get the filtered data set with ages of female promotional customers.

Then find the average   and Standard deviation S of the column ages using the functions =AVERAGE( Select the all ages ) and =STDEV.S( Select the all ages )

So average age   of the female promotional customers = 35.2727

and Standard deviation S female promotional customers age = 12.6635

According to Empirical rule:
Approximately 68% of the observations fall within 1 standard deviation of the mean.
Approximately 95% of the observations fall within 2 standard deviations of the mean.
Approximately 99.7% of the observations fall within 3 standard deviations of the mean.

In part a) we are asked to find lower and upper limit ,between 95% female promotional customer ages should fall.

So according to Empirical rule ,approximately 95% of the observations fall within 2 standard deviations of the mean.

So lower limit = - (2*S) = 35.2727 - ( 2* 12.6635 )

lower limit = 9.9457

So Upper limit = + (2*S) = 35.2727 + ( 2* 12.6635 )

Upper limit = 60.5997

So 95% of female promotional customer ages should be between values ( 9.9457 , 60.5997)

Part b)

We are asked to find lower limit and upper limit , such that between these two limits 68% of the items purchased should be fall.

So first we need to find mean and Standard deviation S for items purchased for all 100 customers.

So we need to remove Filter..so again go to "Data" menu , click on "Filter" and remove the filter .

Then find the mean and Standard deviation S for column items purchased using the same functions.

Now according to Empirical rule , Approximately 68% of the observations fall within 1 standard deviation of the mean.

So lower limit = - (1*S) = 3.22 - ( 1* 2.7361 )

Lower limit = 0.4839

Upper limit = + (1*S) = 3.22 + ( 1* 2.7361 )

Upper limit = 5.9561

68% of items purchased should be between values ( 0.4839 , 5.9561)