You are conducting a study of the relationship between the amount of rain in a field and the total mass of fruit produced by tomato plants. You randomly select tomato plants from a field and weigh all the tomatoes on each plant. You plot the data as a histogram, and the data appear to be normally distributed. You calculate an average weight of 2.6 kg of tomatoes per plant, with a variance of 0.5 kg2. a) You have sampled 50 plants. If you assume your data are normally distributed, what is the probability that the 51st plant you sample has 2.6 kg of tomatoes?
b) What is the probability that the weight of tomatoes on the 51st tomato plant is within +/- one standard deviation of the mean weight of your sample? c) Draw a chart that illustrates the probability the 51st tomato plant has greater than 1.2 kg but less than 3.4 kg total weight of tomatoes? The shape of the function can be approximate.