Question 1 (13 marks)

The times achieved by females to run a marathon were recorded for two different events: an amateur marathon in 2009 in Canada and, secondly, the Olympics in 2008. The data are supplied in a file,Female Marathon Times.xlsx,which can be downloaded from onMoodle in "Assignments" block.

a)Produce a histogram of these combined data and comment on the features of the distribution of times to run a marathon as shown by the histogram.

b)Determine the five-number summary for the each of the two events: amateur Canadian event and, separately, at the 2008 Olympics.

c)Draw a comparative box-plot between the events of the times to run a marathon and comment on any similarities and differences as shown in the comparative box-plot between the different events.

d)Find the mean value of the time in each group and compare each to the medians found. What does each of these comparisons indicate about the distributions?

e)What is the probability that an amateur female marathon runner finishes in a shorter time than the slowest Olympic female runner. Were the conditions OK for this calculation to be done using z-scores?