Question

1. A town’s January high temperature averages 36 o F with a standard deviation of 10 o F, while in July the mean high temperature is 74 o F with standard deviation 8 o F. In which month is it more unusual to have a day with a high temperature of 55 o F? Explain your reasoning. Make sure to compute the z-scores for each temperature to help you compare.

Answer 1

Solution :

Given that ,

mean = = 360 F ( january )

standard deviation =  = 100 F

x = 550 F

Using z-score formula,

z = x - /   

z = 55 - 36 / 10

z = 1.90 ( january )

mean = = 740 F ( july )

standard deviation =  = 80 F

x = 550 F

Using z-score formula,

z = x - /   

z = 55 - 74 / 8

z = -2.37 ( july )

July month is more unusual, because z-score -2.37 is less than z-score -2.00