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.
orchestra answered 1 year agoRelated Solutions
(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
(% 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...
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(c)
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