In a certain cross country running competition the times that each of the 136 runners took to complete the course were recorded to the nearest minute. The winner completed the course in 23 minutes and the final runner came in with a time of 78 minutes. The full results are summarised in the table below. Recorded time Frequency 20-29 30-39 40-49 50-59 60-69 70-79 7 21 42 37 20

(a) Use linear interpolation to estimate the median time. The upper and lower quartiles of the time taken are 58.1 and 40.9 respectively.

(b) On graph paper, draw a box and whisker plot for the results from this competition. Y should mark the end points, the median and the quartiles clearly on your diagram.

(c) Comment on the skewness. Assume that the time taken by the runners to complete the course follows a normal distribution with the values for the quartiles as given above.

(d) Calculate the mean of this normal distribution.

(e) Calculate the standard deviation of this normal distribution.