Problem 8 [10 points = 2+2+2+2 + 2] Department of Public Safety analysts believe that the...

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Problem 8 [10 points = 2+2+2+2 + 2] Department of Public Safety analysts believe that the average car collision rate per day at a busy inter- section is 0.5 per day. The number of collisions during an observation period of NINE days is denoted as M. Use cumulative probabilities for Poisson distribution (Table 2) to answer questions below. 1. Determine the chance to have more than FIVE collisions, P [M > 5] 2. Find how likely is to have at least FIVE collisions, P [M 5] 3. Find probability of having fewer than FIVE collisions, P [M < 5] 4. Derive how likely it is to have exactly FIVE collisions, P[M=5] = 5. Derive the chance that there will be 4 to 8 collisions, including the endpoints, P [4 M 8] Solution Problem 8 [10 points = 2+2+2+2 + 2] Department of Public Safety analysts believe that the average car collision rate per day at a busy inter- section is 0.5 per day. The number of collisions during an observation period of NINE days is denoted as M. Use cumulative probabilities for Poisson distribution (Table 2) to answer questions below. 1. Determine the chance to have more than FIVE collisions, P [M > 5] 2. Find how likely is to have at least FIVE collisions, P [M 5] 3. Find probability of having fewer than FIVE collisions, P [M < 5] 4. Derive how likely it is to have exactly FIVE collisions, P[M=5] = 5. Derive the chance that there will be 4 to 8 collisions, including the endpoints, P [4 M 8] Solution