The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0C at the freezing point of water. Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0C (denoted by negative numbers) and some give readings above 0C (denoted by positive numbers). Assume that the mean reading is 0C and the standard deviation of the readings is 1.00C. Also assume that the frequency distribution of errors closely resembles the normal distribution. A thermometer is randomly selected and tested. Find the temperature reading corresponding to the given information. 5) If 6.3% of the thermometers are rejected because they have readings that are too high and another 6.3% are rejected because they have readings that are too low, find the two readings that are cutoff values separating the rejected thermometers from the others. Sketch the normal distribution curve and identify the indicated areas on the graph. Round your answer to two decimal places. Find the indicated probability. 6) A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. a) If an applicant is randomly selected, find the probability of a rating that is between 170 and 220 using a graphing calculator or other statistical software. Round your answer to four decimal places. b) Find the two z-scores corresponding to ratings of 170 and 220, respectively. c) Verify that the probability between the two z-scores found in Part b) is the same as tthe probability found in Part a). Round your answer to four decimal places. d) Find the ratings corresponding to a z-score of -1.96 and a z-score of 1.96.