Question

In: Statistics and Probability

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

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.

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

Solutions

Expert Solution

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              
(% 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 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
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 -16.0 -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.


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