Question

The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0 degrees Celcius 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 degrees celcius (denoted by negative numbers) and some give readings above 0 degrees celcius (denoted by positive numbers).

Assume that the mean reading is 0 degrees celcius and the standard deviation of the readings is 1.00 degrees celcius. 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.
I know the answer, but do not how to solve the problem. answ-->-1.48

Find the z-value with a left tail of 7%:

invNorm(0.07) = -1.48

Find the termperature deviation that corresponds to that z-value:
x = z*s + u
x = -1.48*1 + 0 = -1.48

Answer 1

Explanation:

Given that reading on thermometer is N (0,1)

7% of the thermometers are rejected because they have readings that are too low, but all other thermometers are acceptable

This implies that we have to find out the 7th percentile.

i.e. Z score = -1.475

Hence the temperature for cutoff is below -1.475 degrees.

the temperature reading corresponding to the given information.=-1.475 deg