The Precision Scientific Instrument Company manufactures thermometers that are s

Question

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 degree 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 0 degree C (denoted by negative numbers) and some give readings above 0 degree C (denoted by positive numbers). Assume that the mean reading is 0 degree C and the standard deviation of the readings is 1.00 degree C. 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. If 7% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.

Explanation / Answer

Given,

Mean = 0 and SD = 1

So,

We need to find the probability P(z < k) = 0.07

From normal distribution table,

P(z < -1.48) = 0.07

Hence,

The temperature which separated the rejected 7% is -1.48 Degree Celsius.

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