Question

A refrigerator runs at a mean temperature of 2.5 degrees Celsius with a standard

deviation of 0.8 degrees Celsius. The manufacturers want to also sell the
refrigerator in countries that use degrees Fahrenheit, so they convert the data by
applying the formula to each data point: Fahrenheit = 9/5 (Celsius) + 32. If each
temperature is converted to degrees Fahrenheit, what will the mean and
standard deviation of the data of the new temperatures be? *

Answer 1

After converting from Celsius to Fahrenheit, the new mean temperature of the refrigerator is 36.5°F, and the standard deviation is 1.44°F.

Step-by-step explanation:

When converting temperatures from Celsius to Fahrenheit using the formula Fahrenheit = (9/5 * Celsius) + 32, only the mean temperature will be directly affected by the addition of 32. The standard deviation will be scaled by the multiplication factor but not affected by the additive constant. Therefore, the mean temperature in Fahrenheit is calculated by converting the mean Celsius temperature: (9/5 * 2.5°C) + 32 = 36.5°F. Now, for the standard deviation, since the conversion factor from Celsius to Fahrenheit is 9/5, we multiply the standard deviation in Celsius by this factor. Thus, the standard deviation in Fahrenheit is 0.8°C * 9/5 = 1.44°F. As a result, the new mean temperature is 36.5°F with a standard deviation of 1.44°F.