题目
Problem
The number of breakdowns on a particular section of road is recorded each day over a period of 90 days. It is suggested that the number of breakdowns follows a Poisson distribution with mean 3.5. The data is summarised in the table, together with some of the expected frequencies resulting from the suggested Poisson distribution.
| Number of breakdowns per day | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 or more |
|---|---|---|---|---|---|---|---|---|---|
| Observed frequency | 0 | 5 | 13 | 17 | 21 | 16 | 9 | 5 | 4 |
| Expected frequency | 2.718 | 9.512 | 16.646 | 16.993 | 11.895 | 3.469 | 2.407 |
(a) Complete the table.
[2]
(b) Carry out a goodness of fit test, at the 10% significance level, to determine whether or not is a good fit to the data.
[6]
题目中文翻译
在 90 天内，每天记录某一路段发生故障的次数。有人提出，故障次数服从均值为 3.5 的泊松分布。数据汇总在下表中，同时给出由所提出的泊松分布得到的一些期望频数。
| 每天故障次数 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 或更多 |
|---|---|---|---|---|---|---|---|---|---|
| 观测频数 | 0 | 5 | 13 | 17 | 21 | 16 | 9 | 5 | 4 |
| 期望频数 | 2.718 | 9.512 | 16.646 | 16.993 | 11.895 | 3.469 | 2.407 |
(a) 完成表格。
(b) 在 10% 显著性水平下进行拟合优度检验，判断 是否很好地拟合该数据。