Question

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give reading is 0degree Celsius 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 0degree Celsius and some give readings above 0degree Celsius. Assume that the mean reading is 0degree Celsius and the standard deviation of the readings is 1.00degree Celsius. 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 9% 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.

_ degree Celsius

Round answer two decimal places.

Answer 1

Solution:

Given: Tests on a large sample of these thermometers reveal that at the freezing point of water, some give readings below 0 degree Celsius and some give readings above 0 degree Celsius. The mean reading is 0 degree Celsius and the standard deviation of the readings is 1.00 degree Celsius.

Also assume that the frequency distribution of errors closely resembles the normal distribution.

That is: X follows Normal distribution

9% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable.

We have to find the temperature that separates the rejected thermometers from the others.

That is we have to find x value such that:

P( X < x ) = 9%

P( X< x) =0.09

Thus find z value such that: P( Z < z) =0.09

Look in z table for area = 0.0900 or its closest area and find corresponding z value.

Area 0.0901 is closest to 0.0900 and it corresponds to -1.3 and 0.04

thus z = -1.34

Now use following formula to find x value.

Thus the temperature that separates the rejected thermometers from the others is -1.34 degree Celsius.