Question

A study was conducted on shoe sizes of students, reported in European sizes. For the women, the mean sie was 39.84 with a standard deviaiton of 1.63. To convert European shoe sizes to U.S. sizes for women, use the equation shown below.

USsize= EuroSize x 0.7882-22.2

a) What is the mean women's shoe size for these responses in U.S. units?

b) What is the standar deviation in U.S. units?

Answer 1

X: European sizes

Mean for European size = E(EuroSize) = 39.84

The standard deviation for European size = std(EuroSize) = 1.63

The equation is USsize= EuroSize x 0.7882 - 22.2

a) We have to find the mean womens shoe size for given reponses in U.S. units.

E(USsize) = E(EuroSize) * 0.7882 - 22.2

E(USsize) = 39.84*0.7882 - 22.2 = 9.2019

9.2019 is the mean womens shoe size for given reponses in U.S. units.

b) Now we have to find standard deviation in U.S. units.

std(USsize) = std(EuroSize)*0.7882 = 1.63*0.7882 = 1.2848

1.2848 is the standard deviation in U.S. units.