Assume that a procedure yields a binomial distribution with a
trial repeated n=17n=17 times.
Use the binomial probability formula to find the probability of
k=3k=3 successes given the probability p=p=1/4 of success on a
single trial.
(Report answer accurate to 4 decimal places.)
P(X=3)=
Solution
Given that ,
p = 1 / 4 = 0.25
1 - p = 1 - 0.25 = 0.75
n = 17
x = 3
Using binomial probability formula ,
P(X = x) = ((n! / x! (n - x)!) * px * (1 - p)n - x
P(X = 3) = ((17! / 3! (17 - 3)!) * 0.2517 * (0.75)17 - 3
= ((17! / 3! (14)!) * 0.2517 * (0.75)14
P(X = 3) = 0.1893
Probability = 0.1893
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