The Precision Scientific Instrument Company manufactures thermometers which are supposed to give readings of 0o C 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 0o C (denoted by negative numbers) and some give readings above 0o C (denoted by positive numbers). Assume that the mean reading is 0o C and the standard deviation of the readings is 1o C. Also assume that the frequency distribution of errors closely resembles the normal distribution. If 9% of the thermometers are rejected because they have readings that are too high, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others. Use two decimal places. Do not use any words or the degree symbol in your answer.
Solution. Denote by X the temperature. So, X follows standard normal ...
This solution shows how to calculate the temperature that separates the rejected thermometers from the others.