Question

Write and solve a probability problem that combine two different probability distributions in the same probelm explain your problem and calculations

Answer 1

Solletion 1 Given data: consider the following problem. Suppose cere normally speed of cars on a highway distributed with mean of goki km Hoor and standard deviation of 15km shor, on any day, gt 70 vehicles pass a cheupost which has manimum speed limit of 126 kmitor, find the probability that there are offenders That day: le than 3 solution: this is combination of normal and binomial probability distribution As speed is normally distributed with mean l=90kmph and 6= 15kmph, co it'x is the speed of a sandomly Chosen vehicule Then: X~ N (6) probability of a candoruly chosen vehicle that its speed is about 128 kmph is, And

2 p(x>120) |- P(x5120) = 1-P (za 120-90 15 I-P (222) 1 -0.9272 6.0228 MDW, as each vehicle can independently have its speed goeater than 120kmph, so distribution of number of overspeeding vehicles out of 10 would follow binomial distribution with parameter a n=10 and P > 0.0228 SO, p(y=x) = (16) (0.0228) (0.9772/10-Y thus, probcubility that dess Theen 3 vehicules are found ousspeeding ist P (123) = ply=o) + P (y=1)+ p (4=2) (0) (0.0228 )* (0-997230 + (19)(0.6228) (0.997239 +19(0-02283 (0.977278 +

» (0.4973€ (0-9972)+(10) (0-228)60.9272)+(45)(623) 0.9987 thes, ore qwiard probability that there would he less than 3 offendere 0.9987 please give nu thumb up