Question

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.

Answer 1

(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.