The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of $0 ^ { \circ } \mathrm { C }$ 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 $0 ^ { \circ } \mathrm { C }$ (denoted by negative numbers) and some give readings above $0 ^ { \circ } \mathrm { C }$ (denoted by positive
numbers). Assume that the mean reading is $0 ^ { \circ } \mathrm { C }$ and the standard deviation of the readings is $1.00 ^ { \circ } \mathrm { C }$ 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 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.
A) 1.26°
B) 1.39°
C) 1.34°
D) 1.45°

Question

Quizplus · Accepted Answer

Since we are given that the frequency distribution of errors closely resembles the normal distribution, we can use the standard normal distribution to solve both parts of the problem.

Part 1:

We are asked to find the temperature reading corresponding to a randomly selected thermometer. Specifically, we want to find the temperature reading that has 50% of the readings below it and 50% above it (i.e. the median reading). Since the mean is given to be 0°C and the standard deviation is given to be 1.00°C, we can use the standard normal distribution to find the z-score corresponding to the median reading:

z = 0

From the standard normal distribution table, we can look up the value of x that corresponds to a z-score of 0:

x = 0°C

Therefore, the temperature reading corresponding to the given information is 0°C.

Part 2:

We are asked to find the temperature that separates the 9% of thermometers that are rejected for having readings that are too high, from the 91% of thermometers that are still acceptable. Since we are dealing with the right tail of the distribution (i.e. high readings), we want to find the temperature reading that corresponds to the 91st percentile of the distribution. We can use the standard normal distribution to find the z-score corresponding to the 91st percentile:

z = 1.34

From the standard normal distribution table, we can look up the value of x that corresponds to a z-score of 1.34:

x = 1.34°C

Therefore, the temperature reading that separates the rejected thermometers from the others is 1.34°C.

The answer is C.

The Precision Scientific Instrument Company Manufactures Thermometers That Are Supposed 0∘C0 ^ { \circ } \mathrm { C }0∘C

The Precision Scientific Instrument Company Manufactures Thermometers That Are Supposed $0 ^ { \circ } \mathrm { C }$