Question

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. A quality control analyst wants to examine thermometers that give readings in the bottom​ 4%. Find the temperature reading that separates the bottom​ 4% from the others. Round to two decimal places.

Answer 1

the temperature reading that separates the bottom​ 4% from the others is -1.75°

Explanation:

The summary of the given statistics data set are:

Mean
`\mu` : 0

Standard deviation
`\sigma` = 1

Probability of the thermometer readings = 4% = 0.04

The objective is to determine the temperature reading that separates the bottom​ 4% from the others

From the standard normal table,

Z score for the Probability P(Z < z) = 0.04

P(Z < -1.75) = 0.04

z = -1.75

Now, the z- score formula can be expressed as :

`z = (X-\mu)/(\sigma)`

`-1.75 = (X-0)/(1)`

-1.75 × 1 = X - 0

X = -1.75 × 1 - 0

X = -1.75

Therefore, the temperature reading that separates the bottom​ 4% from the others is -1.75°