After class, you meet with your friend who scored 0.32 standard deviations below the mean on the same test that you scored 0.71 standard deviations above the mean. What proportion of students scored between your two scores?

What will be an ideal response?

(i) 38.66%; (ii) From the prior problem, you know that the probability associated with a z-score of 0.71 is 0.2611. Knowing that the probability of being below the mean is 0.5000, you find the probability associated with your friend’s z-score of -0.32: P(z=-0.32)=0.1255. Given that you want to determine the probability of being in the range between each z-score and the mean, you add 0.2611 and 0.1255.