1. A manufacturer of scientific instruments produces thermometers that measure the freezing point of water (0 degrees Centigrade). Tests on a large sample have found that some readings are too low (negative values) and some are too high (positive values). If the frequency of a malfunctioning thermometer follows a standard normal distribution. Generate the normal distribution and the cumulative distribution for the thermometer reading in 0.01 degree Centigrade units, including 3 standard deviations on each side of the mean. Graph both of the distribution. Find each of the following probabilities. a) If a thermometer is picked at random, find the probability that, at the freezing level of water, the reading is between 0° and 1.58⁰. b) Find the probability that, at the freezing level of water, the reading is between 0° and -2.43°. c) Find the probability that, at the freezing level of water, the reading is between 1.20° and 2.30°. d) Find the probability that, at the freezing level of water, the reading is greater than 1.27⁰.