Question

Say for a particular population body temperature measured in Celsius has a mean of 37 and the standard deviation is equal to 0.5. What is the mean and standard deviation of the population when temperature is measured in Fahrenheit units?

Answer 1

Answer

given,

Mean of temperature in Celsius = 37    Standard deviation in Celsius = 0.5

relation between Fahrenheit and Celsius

$F = \dfrac{9}{5}C + 32$

Mean of temperature in Fahrenheit

$Mean_F =\dfrac{9}{5}\times Mean_C + 32$

$Mean_F =\dfrac{9}{5}\times 37 + 32$

$Mean_F = 98.6\ F$

Standard deviation of Fahrenheit.

$SD_F = \dfrac{9}{5}\times SD_C$

addition of 32 will not change the Standard deviation.

$SD_F = \dfrac{9}{5}\times 0.5$

$SD_F = 0.9$