The Precision Scientific Instrument compnay manufactures thermometers that are s

Question

The Precision Scientific Instrument compnay 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 poing of water, some give readings below 0C (Denoted by negative numbers) and some give readings above 0C (denoted by posive 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 give information:

A) 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 seperates the rejected thermometers from the others.

B) If 9% of the thermometers are rejected because they have readings that are too low but all other themometers are acceptable, find the temperature that seperates the rejected themometers from the others.

Explanation / Answer

a) here as we know for highest 9% ; at 91th percentile z score =1.34

therefore corresponding temperature =mean +Z*std deviaiton =0+1.34*1 =1.34

b)

for 9th percentile ; z score =-1.34

corresponding temperature =mean +Z*std deviaiton =0-1.34*1 = -1.34

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