Question 1192211: If X~B(8,0.5), find P(X < 4)
Answer by math_tutor2020(3817)   (Show Source):
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X~B(8,0.5) means the random variable X is a binomial random variable with these parameters
n = 8 = sample size
p = 0.5 = probability of success
The probability function is
P(x) = (n C x)*(p)^x*(1-p)^(n-x)
P(x) = (8 C x)*(0.5)^x*(1-0.5)^(8-x)
P(x) = (8 C x)*(0.5)^x*(0.5)^(8-x)
The n C x refers to the nCr combination formula notation.
Plug in x = 0
P(x) = (8 C x)*(0.5)^x*(0.5)^(8-x)
P(0) = (8 C 0)*(0.5)^0*(0.5)^(8-0)
P(0) = (1)*(0.5)^0*(0.5)^8
P(0) = 0.00390625
Repeat for the the x values from x = 1 to x = 3
You should get these results
| X | P(X) | | 0 | 0.00390625 | | 1 | 0.03125 | | 2 | 0.109375 | | 3 | 0.21875 |
Then we can say:
P(X < 4) = P(0) + P(1) + P(2) + P(3)
P(X < 4) = 0.00390625 + 0.03125 + 0.109375 + 0.21875
P(X < 4) = 0.36328125
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