The heights of 200 lilies are normally distributed with a mean of 40 cm and a standard deviation of 3 cm. a Sketch a normal distribution diagram to illustrate this information. Indicate clearly the mean and the heights within one, two and three standard deviations of the mean. b Find the probability that a lily has a height less than 37 cm. c Find the probability that a lily has a height between 37 cm and 46 cm. d Find the expected number of lilies with a height greater than 43 cm.