Normal Distribution

A Wheel Set refers to a set of wheel rim and tyre. The three types of wheel sets are the Clincher Bike Wheel Set, Tubular Bike Wheel Set and Mountain Bike Wheel Set. The weight of a rim of a Clincher Bike Wheel Set follows a normal distribution with mean 1.5 kg and standard deviation 0.01 kg. The weight of its tyre follows a normal distribution with mean 110 g and standard deviation 5 g. (i) Let C be the total weight in grams of a randomly chosen Clincher Bike Wheel Set in grams. Find P(C > 1620) . [3] (ii) State, in the context of the question, an assumption required in your calculation in (i) [1] Let T be the total weight in grams of a Tubular Bike Wheel Set, where T ~ N(u, 152 ). (iii) The probability that the weight of a randomly chosen Clincher Bike Wheel Set exceeds a randomly chosen Tubular Bike Wheel Set by more than 150 g is smaller than 0.70351 correct to 5 decimal places. Find the range of values that / can take. [5] Let M be the total weight in grams of a randomly chosen Mountain Bike Wheel Set with mean 1800 g and standard deviation 20 g. (iv) Find the probability that the mean weight of 50 randomly chosen Mountain Bike Wheel Sets is more than 1795 g. [3]