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 low, but all other thermometers are acceptable, find the temperature that separates the rejected thermometers from the others.
A) -1.45°
B) -1.39°
C) -1.34°
D) -1.26°

Question

Quizplus · Accepted Answer

Since the mean of the readings is $0 ^ { \circ } \mathrm { C }$ and the standard deviation is $1.00 ^ { \circ } \mathrm { C }$, we are dealing with a normal distribution with mean $\mu=0$ and standard deviation $\sigma=1$.

To find the temperature reading that separates the rejected thermometers from the others, we need to find the z-score corresponding to the 9th percentile. We can use a standard normal table or calculator to find that the z-score is approximately -1.34.

Then, we use the formula:

$$z=\frac{x-\mu}{\sigma}$$

where x is the temperature reading we want to find. Plugging in the values we have:

$$-1.34=\frac{x-0}{1}$$

Solving for x, we get:

$$x=-1.34$$

Therefore, the temperature reading that separates the rejected thermometers from the others is approximately -1.34°C, which corresponds to choice 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 $0 ^ { \circ } \mathrm { C }$