The Precision Scientific Instrument Company manufactures thermometers that are supposed to give readings of 0°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°C (denoted by negative numbers) and some give readings above 0°C (denoted by positive numbers). Assume that the mean reading is 0°C and the standard deviation of the readings is 1.00°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.
-A quality control analyst wants to examine thermometers that give readings in the bottom 4%. Find the reading that separates the bottom 4% from the others.
A)-1.63°
B)-1.48°
C)-1.89°
D)-1.75°

Question

Quizplus · Accepted Answer

To find the reading that separates the bottom 4% from the others in a normally distributed set of data, we look for the z-score corresponding to the 4th percentile. Consulting a standard normal (z-score) table or using a statistical calculator, we find that the z-score for the bottom 4% is approximately -1.75. Given that the mean is 0°C and the standard deviation is 1.00°C, a z-score of -1.75 directly translates to a temperature reading of -1.75°C, which separates the bottom 4% of thermometers from the rest.

The Precision Scientific Instrument Company Manufactures Thermometers That Are Supposed