6   2 Shelly works as a project manager for a clothing design company. She is in charge of a project to produce a new jacket design. A pattern is then made of her design. Shelly sends the pattern to the sample production department to be made into a sample jacket. From past experience, it is known that it should take between 5 and 13 working hours for a sample jacket to be produced from a pattern. The uniform distribution is considered a suitable model for the time taken to produce such a sample jacket from a pattern. A diagram of Shelly’s modelling distribution is shown in Figure 2. 5 13 0.125 Probability density (per hour) Number of working hours Figure 2 (a) Explain why the height of the modelling distribution in Figure 2 is 0.125 (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ Turn over 7   Question 2 continued Use Shelly’s model and Figure 2 to answer parts (b) to (e). (b) State the expected time that it will take to produce her sample jacket from the pattern. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (c) State the probability that it will take less than 4 hours to produce her sample jacket from the pattern. (1) _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________