Joan's finishing time for the Bolder Boulder 10k race was 1.71 standard deviations faster than the women's average for her age group. There were 375 women who ran in her age group. Assuming a normal distribution, how many women ran faster than Joan
According to the normal distribution tabulated above, the percentage of scores above average and below 1.71 standard deviations to the right of the mean is 45.64. To find the percetage faster than 1.71 standard deviations, we subtract this from 50% to get
50 - 45.64 = 4.36%.
This means that 4.36 % of the 375 women ran faster than Joan. That is approximately 16 or 17 women:
(.0436)(375) = 16.35