Question

求解一道微积分题，需要“过程”，高分悬赏

The speeds of vehicles on a highway with a speed limit of 80km/h are normally distributed with a mean of 83km/h and standard deviation of 4km/h.
A. What is the probability that a car chosen at random is traveling at an illegal speed?
B. If police are to ticket anyone driving at more than 88km/h or at less than 75km/h, then what percentage of motorists will be ticketed?
翻译（不确定是否准确，如果您懂英文就请忽视）：
80km/h限速的公路上的汽车的速度分布在平均83km/h，标准差是4km/h。
A，随机选择的一辆车有多大几率是超速的？
B，如果警察打算给超过88km/h以及低于75km/h的车罚单的话，有百分之多少的车会被罚？

Answer 1

X~N(83,16),(X-83)/4~N(0,1)
A，随机选择的一辆车有多大几率是超速的？
P(X>80)=P((X-83)/4>(80-83)/4)=1-Φ(-3/4)=Φ(0.75)=0.7734
B，如果警察打算给超过88km/h以及低于75km/h的车罚单的话，有百分之多少的车会被罚？
P(X>88)=P((X-83)/4>(88-83)/4)=1-Φ(5/4)=1-Φ(1.25)=1-0.8944=0.1055
P(X<75)=P((X-83)/4<(75-83)/4)=Φ(-2)=1-Φ(2)=1-0.97725=0.02275
0.1055+0.02275=0.12825=0.13
有13%的车会被罚