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Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials and the probability of obtaining a success.
P(X>4)
, n=8
, p=0.7
Now that we know P(X>4)=1−P(X≤4)=1−[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)]
, we can calculate each individual probability in the equation using the binomial probability formula with n=8
and p=0.7
. Round your answer to six decimal places, if necessary.
P(X=0)=C08⋅(0.7)0(1−0.7)(8−0)=multi-Line Equations line 2 Text Box
P(X=0)=C(8,0) * (0.7)^0 * (1-0.7)^(8-0)
P(X=0)= 1 * 1 * 0.00000297
P(X=0)= 0.00000297
Next, we calculate P(X=1):
P(X=1)=C(8,1) * (0.7)^1 * (1-0.7)^(8-1)
P(X=1)= 8 * 0.7 * 0.0021
P(X=1)= 0.0336
Continuing this process for P(X=2), P(X=3), and P(X=4), and then plug these values back into the equation P(X>4)=1−[P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)]:
P(X>4) = 1 - [0.00000297 + 0.0336 + (calculate P(X=2) + P(X=3) + P(X=4))]
P(X>4) = 1 - [0.00000297 + 0.0336 + (calculate P(X=2) + P(X=3) + P(X=4))]
Please proceed with the calculation for P(X>4) accordingly.