(b) Determine the proportion of the Revenue Growth data that lies within 1, 2, and 3...

(b) Determine the proportion of the Revenue Growth data that lies within 1, 2, and 3 standard deviations of the mean. Determine, using the empirical rule, if the Revenue Growth data is approximately normally distributed.

Company Name	Revenue Growth
Company Name	(% in last year)
Abercrombie & Fitch Co.	2.7
American Eagle Outfitters	2.5
bebe stores, inc.	10.0
Birks Group Inc	5.3
BJs Wholesale Club Holdings Inc	3.4
Boot Barn Holdings Inc	12.7
Bravada International Ltd.	-4.7
Buckle Inc	-14.9
Burlington Stores Inc	-13.5
Cache Inc	-9.9
Caleres Inc	-10.8
Cato Corp	9.2
Chico's FAS, Inc.	10.4
Childrens Place Inc	-16.0
Christopher & Banks Corporation	8.9
Citi Trends, Inc.	-9.9
Companhia Brasileira de Distribuicao	25.7
Costco Wholesale Corporation	1.6
Designer Brands Inc	-0.2
Destination Maternity Corp	-15.1
Dillard's, Inc.	-2.4
Express, Inc.	-9.9
Foot Locker, Inc.	-0.9
Francesca's Holdings Corp	24.8
Gap Inc	2.4
Genesco Inc.	-3.3
Guess?, Inc.	-4.5
J C Penney Company Inc	-4.5
J.Jill Inc	-5.4
Kohl's Corporation	4.4
L Brands Inc	8.7
Macy's Inc	-8.7
Nordstrom, Inc.	-5.2
PriceSmart, Inc.	0.4
Qingco Inc	-35.8
Ross Stores, Inc.	2.6
RTW Retailwinds Inc	0.1
Sears Holdings Corp	-0.5
Shoe Carnival, Inc.	8.8
Stage Stores Inc	52.4
Stein Mart, Inc.	3.7
Tailored Brands Inc	-4.3
Tandy Leather Factory, Inc.	-9.9
Tilly's Inc	7.2
TJX Companies Inc	3.3
Urban Outfitters, Inc.	0.8
Walmart Inc	-3.5
Zumiez Inc.	-8.1

Expert Solution

There are 48 data points

by 68-95-99.7 rule,

68% lies within 1 sd, 95% lies within 2 sd , and 99.7 % lies within 3 sd of mean

using given data

Company Name	Revenue Growth
Company Name	(% in last year)	z-score	\|z\| < 1	\|z\| < 2	\|z\| < 3
Abercrombie & Fitch Co.	2.7	0.19	1	1	1
American Eagle Outfitters	2.5	0.18	1	1	1
bebe stores, inc.	10	0.76	1	1	1
Birks Group Inc	5.3	0.39	1	1	1
BJs Wholesale Club Holdings Inc	3.4	0.25	1	1	1
Boot Barn Holdings Inc	12.7	0.97	1	1	1
Bravada International Ltd.	-4.7	-0.38	1	1	1
Buckle Inc	-14.9	-1.17	0	1	1
Burlington Stores Inc	-13.5	-1.06	0	1	1
Cache Inc	-9.9	-0.78	1	1	1
Caleres Inc	-10.8	-0.85	1	1	1
Cato Corp	9.2	0.70	1	1	1
Chico's FAS, Inc.	10.4	0.79	1	1	1
Childrens Place Inc	-16	-1.25	0	1	1
Christopher & Banks Corporation	8.9	0.67	1	1	1
Citi Trends, Inc.	-9.9	-0.78	1	1	1
Companhia Brasileira de Distribuicao	25.7	1.97	0	1	1
Costco Wholesale Corporation	1.6	0.11	1	1	1
Designer Brands Inc	-0.2	-0.03	1	1	1
Destination Maternity Corp	-15.1	-1.18	0	1	1
Dillard's, Inc.	-2.4	-0.20	1	1	1
Express, Inc.	-9.9	-0.78	1	1	1
Foot Locker, Inc.	-0.9	-0.09	1	1	1
Francesca's Holdings Corp	24.8	1.90	0	1	1
Gap Inc	2.4	0.17	1	1	1
Genesco Inc.	-3.3	-0.27	1	1	1
Guess?, Inc.	-4.5	-0.36	1	1	1
J C Penney Company Inc	-4.5	-0.36	1	1	1
J.Jill Inc	-5.4	-0.43	1	1	1
Kohl's Corporation	4.4	0.32	1	1	1
L Brands Inc	8.7	0.66	1	1	1
Macy's Inc	-8.7	-0.69	1	1	1
Nordstrom, Inc.	-5.2	-0.42	1	1	1
PriceSmart, Inc.	0.4	0.01	1	1	1
Qingco Inc	-35.8	-2.79	0	0	1
Ross Stores, Inc.	2.6	0.18	1	1	1
RTW Retailwinds Inc	0.1	-0.01	1	1	1
Sears Holdings Corp	-0.5	-0.05	1	1	1
Shoe Carnival, Inc.	8.8	0.66	1	1	1
Stage Stores Inc	52.4	4.04	0	0	0
Stein Mart, Inc.	3.7	0.27	1	1	1
Tailored Brands Inc	-4.3	-0.35	1	1	1
Tandy Leather Factory, Inc.	-9.9	-0.78	1	1	1
Tilly's Inc	7.2	0.54	1	1	1
TJX Companies Inc	3.3	0.24	1	1	1
Urban Outfitters, Inc.	0.8	0.05	1	1	1
Walmart Inc	-3.5	-0.29	1	1	1
Zumiez Inc.	-8.1	-0.64	1	1	1

	0.210416667	frequency	40	46	47
	12.9299461	proportion	0.833	0.958	0.979

hence 83.3 % lies within 1 sd,

95.8 % within 2 sd

97.9 % within 3 sd

we see that there is high proportion of data within 1 sd

hence the Revenue Growth data is not approximately normally distributed.

orchestra answered 1 year ago

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