SOLUTION: You sneak into the gradebook to see how you are performing compared to your fellow classmeates. You learn that the mean score on the first exam was an 84 with a standard deviation

Question 1031674: You sneak into the gradebook to see how you are performing compared to your fellow classmeates. You learn that the mean score on the first exam was an 84 with a standard deviation of 16.
a. what is the z-score corresponding to a score of 81? How do you interpret the score?
b. What is the probability that someone would score a 60 or lower?
c. what is the probability that someone would score between an 80 or 90?
Answer by adunbar(3) (Show Source): You can put this solution on YOUR website!
a. What is the z-score corresponding to a score of 81? How do you interpret the score? The z score is 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%

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