Answer:
The required probability is 0.9916
Step-by-step explanation:
Consider the provided information.
If 45% of cars are traveling in excess of 70mph,
Therefore, p = 0.45
q = 1-p = 1-0.45 = 0.55
8 random cars are measured via radar: n = 8
We need to find at least 1 car is going over 70mph.
According to binomial distribution: [tex]P(X=x)=^nC_rp^rq^{n-r}[/tex]
We need to find P(X≥1)
[tex]P(X\geq 1)=1-P(X=0)[/tex]
[tex]P(X\geq 1)=1-^8C_0(0.45)^0(0.55)^{8-0}[/tex]
[tex]P(X\geq 1)=1-(0.55)^{8}[/tex]
[tex]P(X\geq 1)=1-0.0084[/tex]
[tex]P(X\geq 1)=0.9916[/tex]
Hence, the required probability is 0.9916
