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5.2 Standard Normal Distribution Notes Notes 1.) A college dean must select a starting time between 0 and 5 hours, and the selection is made in such a way that all possible outcomes are equally likely. If she randomly selects a starting time, what is the probability that it is during the first half hour or the last half hour? 2.) The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of zero degrees Celsius at freezing point of water. Tests on large sample of these instruments reveal that at the freezing point of water, some thermometers give readings below zero degrees and some above zero degrees. Assume that the mean reading is zero degrees Celsius and standard deviation of readings is 1.00 degrees Celsius. Also assume that the readings selected are normally distributed. If one thermometer is randomly selected, find the probability that, at the freezing point of water, the reading is between 0 and +1.58 degrees Celsius. 3.) From the example above, find the probability of randomly selecting one thermometer that reads between -2.43 degrees and 0 degrees. ***Although a z-score can be negative, the area under the curve can never be negative. 4.) Once again, make a random selection from the same sample of thermometers. Find the probability that the chosen thermometer reads (at freezing point of water) more than +1.27 degrees. 5.) Assuming that one thermometer in our sample is randomly selected, find the probability that it reads (at freezing point of water) between 1.20 degrees and 2.30 degrees. Notes 6.) Use the same thermometers as earlier, with temperature readings that are normally distributed with a mean of 0 degrees Celsius and a standard deviation of 1.00 degrees Celsius. Find the temperature corresponding to P95, the 95th percentile. That is, find the temperature separating the bottom of 95% from the top 5%. 7.) Using the same thermometer, find P10.