A family was asked to record the number of letters delivered to their house on each of 200 randomly chosen weekdays. The results are summarised below:

a. It is suggested that the number of letters delivered each weekday has a Poisson distribution. By finding the mean and variance for this sample, comment on the appropriateness of this suggestion.

The following table includes some of the expected values, correct to 3 decimal places, using a Poisson distribution with mean equal to the sample mean for the above data.

b. i. Show that p = 46.304, correct to 3 decimal places, and find g.

ii. Carry out a goodness of fit test at the 10% significance level. 

Transcribed Image Text:

Number of letters 2 3 4 5 >6 Number of days 57 60 53 25 4