Answer:
[tex]P(x < 4) = 0.0152[/tex]
Step-by-step explanation:
We are given a binomial distribution.
P(Success) = p = 0.6
We can calculate probability as:
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}[/tex]
where n is the total number of observations, x is the number of success, p is the probability of success.
Now, we are given n = 12
We have to evaluate:
[tex]P(x < 4) \\= P(x = 0) + P(x = 1) + P(x = 2)+P(x = 4) \\= \binom{12}{0}(0.6)^0(1-0.6)^{12} +...+ \binom{12}{3}(0.6)^3(1-0.6)^{9}\\= 0.00001+0.0003+0.0024+0.01245\\= 0.0152[/tex]
0.0152 is the required probability.
