Mathematics, 06.06.2020 01:00 ghwolf4p0m7x0
Harper's Index reported that the number of (Orange County, California) convicted drunk drivers whose sentence included a tour of the morgue was 506, of which only 1 became a repeat offender.
a. Suppose that of 1056 newly convicted drunk drivers, all were required to take a tour of the morgue. Let us assume that the probability of a repeat offender is still p= 1/596. Explain why the Poisson approximation to the binomial would be a good choice for r = number of repeat offenders out of 963 convicted drunk drivers who toured the morgue.
The Poisson approximation is good because n is large, p is small, and np < 10.The Poisson approximation is good because n is large, p is small, and np > 10. The Poisson approximation is good because n is large, p is large, and np < 10.The Poisson approximation is good because n is small, p is small, and np < 10. What is λ to the nearest tenth?
b. What is the probability that r = 0? (Use 4 decimal places.)
c. What is the probability that r > 1? (Use 4 decimal places.)
d. What is the probability that r > 2? (Use 4 decimal places.)
e. What is the probability that r > 3? (Use 4 decimal places.)
Answers: 2
![P(r1)=1-P(r\leq1)=1-[P(r=0)+P(r=1)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\\\P(r1)=1-(0.2019+0.3230)=1-0.5249=0.4751](/tpl/images/0678/1009/b4531.png)
![P(r2)=1-P(r\leq2)=1-[P(r=0)+P(r=1)+P(r=2)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\P(2)=1.6^{2} \cdot e^{-1.6}/2!=2.56*0.2019/2=0.2584\\\\\\P(r2)=1-(0.2019+0.3230+0.2584)=1-0.7833=0.2167](/tpl/images/0678/1009/950e8.png)
![P(r3)=1-P(r\leq2)=1-[P(r=0)+P(r=1)+P(r=2)+P(r=3)]\\\\\\P(0)=1.6^{0} \cdot e^{-1.6}/0!=1*0.2019/1=0.2019\\\\P(1)=1.6^{1} \cdot e^{-1.6}/1!=1.6*0.2019/1=0.3230\\\\P(2)=1.6^{2} \cdot e^{-1.6}/2!=2.56*0.2019/2=0.2584\\\\P(3)=1.6^{3} \cdot e^{-1.6}/3!=4.096*0.2019/6=0.1378\\\\\\P(r3)=1-(0.2019+0.3230+0.2584+0.1378)=1-0.9211=0.0789](/tpl/images/0678/1009/022ad.png)
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Harper's Index reported that the number of (Orange County, California) convicted drunk drivers whose...
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