Step-by-step explanation:
Given:
p=54 %=0.54
n=8
DEFINITIONS
Definition binomial probability:
[tex]P(X=x)=\frac{n !}{x !(n-x) !} \cdot p^{x} \cdot(1-p)^{n-x}[/tex]
Complement rule:
P( not A) = 1- P(A)
[tex]Addition rule for disjoint or mutually exclusive events[/tex]
[tex]P(A \text { or } B)=P(A)+P(B)[/tex]
Evaluate the definition of binomial probability at x=6
[tex]P(X=6)=\frac{8 !}{6 !(8-6) !} \cdot 0.54^{6} \cdot(1-0.54)^{8-6}=28 \cdot 0.54^{6} \cdot 0.46^{2} \approx 0.1469[/tex]
