Question 3 (20 marks) The watermelons from Yahya's Farm follow a normal distribution with a mean of 1.3 kg and a standard deviation of 0.85 kg. a) Sketch a diagram of the normal distribution curve showing the probability that a randomly selected watermelon weighs between 1.5 to 1.8 kg. Hence, calculate this probability. (6 marks) b) The heaviest 18.3% of the watermelons weigh X kg or more. Sketch a diagram of the probability distribution showing the position of X in relation to the mean and hence compute the value of X. (6 marks) (i) Based on Empirical rule, sketch a normal distribution curve of the distribution of weights of the watermelons in Yahya's Farm. Show in your diagram, . the value of the mean weight, . the value of the weight at ,u + a and . the value of the weight at p + 20, where p is the mean and a the standard deviation. (4 marks) (ii) Shade the area corresponding to the probability for the interval in part (c)(i) and calculate the percentage of watermelon weights that would fall under it. (1 mark)