According to data from 2015, women's shoe sales in the US are roughly normally distributed by shoe size with a mean of size 8 and a standard deviation of 1.25 sizes. a) If a women's shoe sold in the US is a size 7.5, what is the z-score?

b) What size of women's shoe would have a z-score of 1.3?

c) If a women's shoe sold in the US is a size 9, what is the z-score and percentile? z-score:
Percentile:

d) What size of women's shoe would have a z-score of -1.5? What percentile is that? shoe size:
Percentile:

e) What women's shoe size represents the 80th percentile? z-score:
shoe size: