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Question 6 Question 6 continued... The animals reach the safety of the other side of the river! They are nearly at the Lava Lakes c) Calculate the mean of X as an exact value. Unfortunately, the animals now have to wait for Sid (the Sloth) to wake up before they can walk to the Lakes. A giant sloth's sleeping time, X hours, has a probability density function: f (x) = x(100 -xz) 2500 if O S x S 10 0 otherwise a) Draw the graph of f (x) with the help of your calculator, choosing an appropriate scale, labelling and showing any intercepts and turning points over the domain. The grid below can be used as a d) Calculate the median of X to 2 decimal places. Show all working. guide. 40-251 -0:2 -0.15 -0-1 -0:05 o -0:05 b) Show that is a probability density function. Show all working. e) What do the mean and median tell you about the skewness of the graph? Is this supported by your graph? Explain. Question 6 continued on the next page... Question 6 continued on the next page... Page 11 Page 12