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The Precision Scientific Instrument Company

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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.

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This solution shows how to calculate the temperature that separates the rejected thermometers from the others.

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Solution. Denote by X the temperature. So, X follows standard normal ...

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  • BSc , Wuhan Univ. China
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Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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