For binomial distribute we use formula
the probability mass function of the binomial distribution is:
Given n = 12 and π = .6. (Replace the values)
the probability for x = 5, we need to find P(x=5). Here r= 5
P(x=5)=
= = 0.10090 = 0.101
(b) the probability for x ≤ 5
P(x<=5) = P(x=0) + P(x=1) +P(x=2)+ P(x=3) + P(x=4) + P(x=5)
P(x<=5) = +
+
+
+
+
= 0.15821229 = 0.158
(c) find the probability for x ≥ 6
P(x>=6) =P(x=6) + P(x=7) +P(x=8)+ P(x=9) + P(x=10) + P(x=11)+ P(x=12)
P(x>=6) = +
+
+
+
+
+
= 0.8417877 = 0.0842 (rounded to 3 decimal places)