Answer:
0.2264
0.1795
0.2264
Step-by-step explanation:
Given that:
p = 19% = 0.19
Sample size (n) = 12
Using binomial distribution formula :
p(x = x) = nCx * p^x * (1 - p)^(n-x)
1 - p = 1 - 0.19 = 0.81
Exactly 3:
p(x = 3) = 12C3 * 0.19^3 * 0.81^9
p(x = 3) = 220 * 0.001029499103502116970939
= 0.2264
B.) Atleast 4 :
P( x ≥ 4) = p(4) + p(5) + p(6) + p(7) + p(8) + p(9) + p(10) + p(11) + p(12)
To save time, we can use a binomial probability calculator :
P( x ≥ 4) = 0.1795
C.) Less than 8:
P( x < 8) = p(7) + p(6) + p(5) + p(4) + p(3) + p(2) + p(1) + p(0)
P(x < 8) = 0.9995
