Question 634161
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Hi,
Oh dear...
1) and 2) are ex of Biomonial Probability: P = nCx* {{{p^x*q^(n-x)}}}
 p = 1/2  and q = 1/2 
1a. {{{P(x=3)= 3C3(1/2)^3= 1/8 }}} 
1b. {{{P(x=2) = 3C2(1/2)^2(1/2)^1 = 3/8}}}
1c. {{{P(x=2) + P(x=3) = 1/2}}} 
1d. {{{P(x=0) = 3C0q^3 = 1/8}}}
2a. {{{P(x = 0) = q^3 = 6C0(.8)^3}}}     p = .20  and q = .80
2b. P(x&#8805; 1) = 1 - P(0)
3b. P(no more than two) = 1- P(3) = 1 - (.20)^6
As to 3 - 8, these are ex of normal distribution: {{{z = (x - mu)/(sigma)}}}
recommend finding P(z value) as needed using NORMSDIST Excel function 
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))}}}