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4. In an Olympic triathlon, competitors take part in three events: a 1.5km swimming leg, a 40km cycling leg followed by a 10km run. To attract sponsorship, Jasper needs to perform in the top 15% of times in each leg when compared to the times recorded by the gold medallist. Jasper has already demonstrated he is in the top 15% of times in the cycling leg. For the other two legs, the gold medallist’s swimming time is 17.24 minutes and running time is 31.09 minutes.

Jasper’s running times are Normally distributed with mean 32.83 minutes and standard deviation 1.13 minutes and his swimming times are Normally distributed with mean 17.70 minutes and standard deviation 0.46 minutes. Based on your calculations what recommendations can you make for sponsorship qualification?

(Total of 14 Marks)

Hint! Perform relevant probabilities calculations to answer this question.

Note! For full marks, include an appropriate probability statement for each question and illustrate each calculation with an appropriate diagram. Refer to the Assignments page on the course web site for a file with diagram templates that you can copy and paste into your assignment.

please provide all working - using z Score. I'm trying to get my head around the calculations