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.
-Find Q $\mathrm { Q } _ { 3 }$ , the third quartile.
A) -1.3°
B) 0.67°
C) 0.82°
D) 0.53°

Question

Quizplus · Accepted Answer

Since the mean reading is 0°C and the standard deviation is 1.00°C, we can use a standard normal distribution to find the temperature reading corresponding to the third quartile.

Using a standard normal distribution table or calculator, we can find that the z-score corresponding to the third quartile is approximately 0.67.

We can then use the formula z = (x - μ) / σ, where z is the z-score, μ is the mean (0°C), σ is the standard deviation (1.00°C), and x is the temperature reading we are trying to find.

Rearranging the formula, we get x = μ + zσ = 0 + 0.67(1.00) = 0.67°C.

Therefore, the temperature reading corresponding to the third quartile is 0.67°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 $0 ^ { \circ } \mathrm { C }$