Standard +0.8 This question requires understanding that two independent Poisson distributions sum to another Poisson distribution, converting weekly rates to daily rates (6/5 and 2/5), then calculating P(X > 3) = 1 - P(X ≤ 3) with parameter λ = 8/5. While conceptually straightforward for S3 students, it involves multiple steps including rate conversion, distribution addition, and cumulative probability calculation, making it moderately above average difficulty.
1 A car repair firm receives call-outs both as a result of breakdowns and also as a result of accidents. On weekdays (Monday to Friday), call-outs resulting from breakdowns occur at random, at an average rate of 6 per 5 -day week; call-outs resulting from accidents occur at random, at an average rate of 2 per 5 -day week. The two types of call-out occur independently of each other. Find the probability that the total number of call-outs received by the firm on one randomly chosen weekday is more than 3 .
Poisson model for call-outs with mean \(\frac{1}{2}(6+2) = 1.6\)
B1
For any implication of Poisson
Probability is \(1 - 0.9212 = 0.0788\)
M1
For summing two relevant parameters
A1
For correct mean of 1.6
M1
For relevant use of tables
A1
5
For correct answer
Poisson model for call-outs with mean $\frac{1}{2}(6+2) = 1.6$ | B1 | For any implication of Poisson
Probability is $1 - 0.9212 = 0.0788$ | M1 | For summing two relevant parameters
| A1 | For correct mean of 1.6
| M1 | For relevant use of tables
| A1 | 5 | For correct answer
1 A car repair firm receives call-outs both as a result of breakdowns and also as a result of accidents. On weekdays (Monday to Friday), call-outs resulting from breakdowns occur at random, at an average rate of 6 per 5 -day week; call-outs resulting from accidents occur at random, at an average rate of 2 per 5 -day week. The two types of call-out occur independently of each other. Find the probability that the total number of call-outs received by the firm on one randomly chosen weekday is more than 3 .
\hfill \mbox{\textit{OCR S3 Q1 [5]}}