document.write( "Question 1192211: If X~B(8,0.5), find P(X < 4)
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Algebra.Com's Answer #824108 by math_tutor2020(3817) $\"\"$ $\"About$

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\n" ); document.write( "X~B(8,0.5) means the random variable X is a binomial random variable with these parameters
\n" ); document.write( "n = 8 = sample size
\n" ); document.write( "p = 0.5 = probability of success\r
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\n" ); document.write( "\n" ); document.write( "The probability function is
\n" ); document.write( "P(x) = (n C x)*(p)^x*(1-p)^(n-x)
\n" ); document.write( "P(x) = (8 C x)*(0.5)^x*(1-0.5)^(8-x)
\n" ); document.write( "P(x) = (8 C x)*(0.5)^x*(0.5)^(8-x)
\n" ); document.write( "The n C x refers to the nCr combination formula notation.\r
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\n" ); document.write( "\n" ); document.write( "Plug in x = 0
\n" ); document.write( "P(x) = (8 C x)*(0.5)^x*(0.5)^(8-x)
\n" ); document.write( "P(0) = (8 C 0)*(0.5)^0*(0.5)^(8-0)
\n" ); document.write( "P(0) = (1)*(0.5)^0*(0.5)^8
\n" ); document.write( "P(0) = 0.00390625\r
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\n" ); document.write( "\n" ); document.write( "Repeat for the the x values from x = 1 to x = 3
\n" ); document.write( "You should get these results\n" ); document.write( "\n" ); document.write( "

X	P(X)
0	0.00390625
1	0.03125
2	0.109375
3	0.21875

Then we can say:
\n" ); document.write( "P(X < 4) = P(0) + P(1) + P(2) + P(3)
\n" ); document.write( "P(X < 4) = 0.00390625 + 0.03125 + 0.109375 + 0.21875
\n" ); document.write( "P(X < 4) = 0.36328125
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