Question 2
The probability that a call-centre consultant receives 3 calls during any given hour is 0.1404 and the probability that the consultant receives 5 calls during any given hour is 0.1755. Assuming that the calls are Poisson-distributed, calculate the probability that the consultant receives at least 2 calls during any 30 minute period.
Question 3
A bank with a branch located in the commercial district of a city has developed an improved process for serving customers during the 12:00 to 13:00 peak lunch period. The waiting times, during this period, of all customers was recorded over a period of one week. The waiting times (in min) of 15 randomly-selected customers is given below.
4.21 5.55 3.02 5.13 4.77
2.34 3.54 3.20 4.50 6.10
0.38 5.12 6.46 6.19 3.79
Suppose that another bank located in a residential area is most concerned with the Friday evening hours from 5 to 7. A sample of the waiting times of 15 randomly-selected customers is given in the table below.
9.66 5.90 8.02 5.79 3.82
8.01 8.35 10.49 6.68 5.64
4.08 6.17 9.91 5.47 8.73
Conduct a full test, at the 5% level of significance, to establish whether there is a statistically significant difference between the population mean times in the two banks. (Assume that the samples are drawn from populations that are approximately normally distributed and that their variances are equal.)
Question 4
The managers of a retail giant are preparing revenue plans for the period from October 2013 to March 2014. The data given below represents the amounts (in $m) of one of their main products.
Apr-Jun Jul-Sep Oct-Dec Jan-Mar
2009/10 49 37 58 67
2010/11 50 38 59 68
2011/12 51 40 60 70
2012/13 50 42 - -
Use the moving-average method to make seasonally-adjusted trend estimates for the third and fourth quarters of 2013 and the first two quarters of 2014. Assume that the cyclical and irregular forces have minimal influence on the time series. (Show details of all your calculations.)