Question 1031674
a. What is the z-score corresponding to a score of 81? How do you interpret the score?  The z score is {{{z = (X - x)/s }}} where X = data point, x = mean, s = standard deviation
The z- score is -0.1875 which converts to 46.41%. This means that approximately 47% of the class got better grades, with 53% getting worse grades. The interpretation of this is this student is operating at about the middle of the class. 
In terms of probability, the probability of a score being greater than .4641 is approximately 46.41%.

b. What is the probability that someone would score a 60 or lower? 
The z-score is -1.5 converting to 0.0668 which is 6.68%. So the probability of someone getting lower than 60 is approximately 7%.
 
c. What is the probability that someone would score between an 80 or 90? 
The z-score for 80 is -0.25, which gives .4013 i.e. 40.13%, while that of 90 is 0.375, which gives, .6480, which is 64.80%. Thus the range is 64.8 – 40.13 = 24.67%