Questions: You can convert temperatures in degrees Celsius to degrees Fahrenheit using the formula F = (9/5)C + 32. If a sample of temperatures in Celsius has a mean =22 and standard deviation =2, the mean and standard deviation in Fahrenheit will be:

You can convert temperatures in degrees Celsius to degrees Fahrenheit using the formula F = (9/5)C + 32. If a sample of temperatures in Celsius has a mean =22 and standard deviation =2, the mean and standard deviation in Fahrenheit will be:

Transcript text: You can convert temperatures in degrees Celsius to degrees Fahrenheit using the formula F = (9/5)C + 32. If a sample of temperatures in Celsius has a mean $=22$ and standard deviation =2, the mean and standard deviation in Fahrenheit will be:

Solution

Solution Steps

To convert the mean temperature from Celsius to Fahrenheit, apply the conversion formula directly to the mean. For the standard deviation, since it is a measure of spread and not affected by the addition of a constant, only the multiplication factor in the conversion formula affects it. Therefore, multiply the standard deviation by the factor 9/5.

Step 1: Convert Mean Temperature from Celsius to Fahrenheit

To convert the mean temperature from Celsius to Fahrenheit, use the formula: \[ F = \left(\frac{9}{5}\right)C + 32 \] Given that the mean temperature in Celsius is $22$, substitute this value into the formula: \[ F = \left(\frac{9}{5}\right) \times 22 + 32 = 71.6 \]

Step 2: Convert Standard Deviation from Celsius to Fahrenheit

The standard deviation is only affected by the multiplication factor in the conversion formula, not the addition. Therefore, multiply the standard deviation by $\frac{9}{5}$: \[ \text{Standard Deviation in Fahrenheit} = \left(\frac{9}{5}\right) \times 2 = 3.6 \]