Question 852643
<pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
My point in doing the following is to encourage You to use a spreadsheet or Calculator
The IMPORTANT thing is to <u>relatively easily find the standard deviation</u>, 
so as to not forget the purpose of doing so in the process.
	m	(x-µ)	(x-µ)^2	
42	76.94	-34.94	1220.804	
55	76.94	-21.94	481.364	
55	76.94	-21.94	481.364	
61	76.94	-15.94	254.084	
64	76.94	-12.94	167.444	
65	76.94	-11.94	142.564	
66	76.94	-10.94	119.684	
67	76.94	-9.94	98.804	
68	76.94	-8.94	79.924	
69	76.94	-7.94	63.044	
70	76.94	-6.94	48.164	
71	76.94	-5.94	35.284	
72	76.94	-4.94	24.404	
74	76.94	-2.94	8.644	
76	76.94	-0.94	0.884	
77	76.94	0.06	0.004	
77	76.94	0.06	0.004	
78	76.94	1.06	1.124	
79	76.94	2.06	4.244	
81	76.94	4.06	16.484	
83	76.94	6.06	36.724	
84	76.94	7.06	49.844	
85	76.94	8.06	64.964	
87	76.94	10.06	101.204	
88	76.94	11.06	122.324	
89	76.94	12.06	145.444	
89	76.94	12.06	145.444	
90	76.94	13.06	170.564	
92	76.94	15.06	226.804	
94	76.94	17.06	291.044	
94	76.94	17.06	291.044	
98	76.94	21.06	443.524	
99	76.94	22.06	486.644	
76.93939394	        5823.879  sum	
			181.9962125 =  sum /(33-1)= Variance	
			13.4905971 = (sqrt of Variance) = SD = 13.5
f.How many of the scores are within one standard deviation of the mean?
 Those scores between 76.9-13.5   and 76.9+13.5 
         0r  between 63.4  and 90.4  (Quite a number of them)
For the normal distribution: 
one  standard deviation from the mean accounts for about 68.2% of the set 
two standard deviations from the mean account for about 95.4%
and three standard deviations from the mean account for about 99.7%.
Important to Understand z -values as they relate to the Standard Normal curve:
Below:  z = 0, z = ± 1, z= ±2 , z= ±3 are plotted.  
Note: z = 0 (x value the mean) 50% of the area under the curve is to the left and %50 to the right
{{{drawing(400,200,-5,5,-.5,1.5, graph(400,200,-5,5,-.5,1.5, exp(-x^2/2)), green(line(1,0,1,exp(-1^2/2)),line(-1,0,-1,exp(-1^2/2))),green(line(2,0,2,exp(-2^2/2)),line(-2,0,-2,exp(-2^2/2))),green(line(3,0,3,exp(-3^2/2)),line(-3,0,-3,exp(-3^2/2))),green(line( 0,0, 0,exp(0^2/2))),locate(4.8,-.01,z),locate(4.8,.2,z))}}}