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 P $\mathrm { P } _ { 40 }$ , the 40th percentile.
A) 0.25°
B) 0.57°
C) -0.25°
D) -0.57°

Question

Quizplus · Accepted Answer

As stated in the problem, the mean reading is $0 ^ { \circ } \mathrm { C }$ and the standard deviation is $1.00 ^ { \circ } \mathrm { C }$. Since we are looking for the value at the 40th percentile, we want to find the temperature reading such that 40% of the readings are below it. Using a standard normal distribution table, we find that the z-score corresponding to the 40th percentile is -0.25. Since the temperature readings have a mean of $0 ^ { \circ } \mathrm { C }$ and a standard deviation of $1.00 ^ { \circ } \mathrm { C }$, the temperature corresponding to a z-score of -0.25 is $-0.25 \times 1.00 = -0.25 ^ { \circ } \mathrm { C }$. Therefore, the answer is C, -0.25°.

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 $0 ^ { \circ } \mathrm { C }$