The following is the 10-year record of floods between 1994 and 2003 in Town A. The occurrences of floods in the town may be modelled as a Poisson process. YEAR flood 1994 1 1995 0 1996 1 1997 1 1998 0 1999 0 2000 2 2001 0 2002 0 2003 1
The following is the 10-year record of floods between 1994 and 2003 in Town A. The occurrences of floods in the town may be modelled as a Poisson process.
| YEAR | flood |
| 1994 | 1 |
| 1995 | 0 |
| 1996 | 1 |
| 1997 | 1 |
| 1998 | 0 |
| 1999 | 0 |
| 2000 | 2 |
| 2001 | 0 |
| 2002 | 0 |
| 2003 | 1 |
(1) On the basis of the above historic flood data, determine the probability there will be between 1 and 3 floods in the town over the next 3 years. [Note P(1≤N≤3 within 3 years) = P(N=1 within 3 years) + P(N=2 within 3 years) + P(N=3 within 3 years)]
(2) A sewage treatment plant is located at a high ground in the town. The probability that it will be inundated during a flood is 0.02. What is the probability that the plant will not be inundated for a period of 5 years? [Note the mean rate of flood that would cause inundation = 0.6 x 0.02=0.012]
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