Question
In: Advanced Math
The parlor's second month results show that it made six sales at $25, one at $48,...
The parlor's second month results show that it made six sales at
$25, one at $48, one at $64, three at $76, three at $107, and two at $121.
Calculate the standard deviation for this data set.
Does your answer for the standard deviation indicate that this is a normal distribution? If not, what are the implications?
A.
Yes
More than 68% of the values are within one standard deviation from the mean. This means that future sales will not vary greatly.
B.
No Less than 68% of the values are within one standard deviation from the mean. This means that future sales may vary greatly.Your answer is correct.
C.
No More than 68% of the values are within one standard deviation from the mean. This means that future sales may vary greatly.
D.
Yes Less than 68% of the values are within one standard deviation from the mean. This means that future sales will not vary greatly.
Solutions
Expert Solution
(a)
From the given data the following Table is calculated:
n = 16
= 1053/16 =
65.8125
| x | (x - ) |
(x - )2 |
| 25 | - 40.8125 | 1665.6602 |
| 25 | - 40.8125 | 1665.6602 |
| 25 | - 40.8125 | 1665.6602 |
| 25 | - 40.8125 | 1665.6602 |
| 25 | - 40.8125 | 1665.6602 |
| 25 | - 40.8125 | 1665.6602 |
| 48 | - 17.8125 | 317.2852 |
| 64 | - 1.8125 | 3.2852 |
| 76 | 10.1875 | 103.7852 |
| 76 | 10.1875 | 103.7852 |
| 76 | 10.1875 | 103.7852 |
| 107 | 41.1875 | 1696.4102 |
| 107 | 41.1875 | 1696.4102 |
| 107 | 41.1875 | 1696.4102 |
| 121 | 55.1875 | 3045.6602 |
| 121 | 55.1875 | 3045.6602 |
| Total = | 21806.4375 |
Standard Deviation (s) is given by:
(b)
Total number of data points = 16
Number of data points in 
=
5
So,
Percentage of data points in =
(5/16) X 100 = 31.25%
So,
Correct option:
B. No, Less than 68% of the values are within one standard deviation from the mean. This means that future values may vary greatly.
Colby Messinger answered 2 years agoRelated Solutions
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