| 2.48 | ||||||||||
| t = | 1 | week | ||||||||
| Time Period: | Peak | |||||||||
| Arrival Rate: | 37 | accidents/year | accidents/year | |||||||
| Arrival Rate (u): | 0.71 | accidents/week | accidents/week | |||||||
| P(No vehicles while backing out) = P(H >= 9) | ||||||||||
| P(n)=e-ut(ut)n/n! | ||||||||||
| P(at least 1) = P(n > 0) = 1 - P(n <=0) = 1 - P(0) = 1 - [e-(0.71acc/week)(1 week)][(0.71 acc/week)(1 week)]0/0! | ||||||||||
| P(at least 1) = 1 - 0.492 = 0.508 | ||||||||||
| What is the probability of at least 2 accidents next week? | ||||||||||
| P(at least 2) = P(n > 1) = 1 - P(n <=1) = 1 - {P(0) + P(1)} = 1 - {0.492 + [e-(0.71acc/week)(1 week)][(0.71 acc/week)(1 week)]1/1!} | ||||||||||
| P(at least 2) = 1 - 0.492 - 0.349 = 0.159 | ||||||||||
| What is the probability of exactly 4 accidents next week? | ||||||||||
| P(4) = P(n = 4) = [e-(0.71acc/week)(1 week)][(0.71 acc/week)(1 week)]4/4! | ||||||||||
| P(4) =[(0.492)(0.254)]4/(1*2*3*4) | ||||||||||
| P(4) = 0.005 | ||||||||||