The following problems reflect the reading material you had to prepare for this week. From the list below, choose one problem, write it down, and solve it in detail (show all of your steps). You should pick a problem that has not yet been attempted if you can. Please label your solution with the corresponding question number. In your solutions, you are only to use the math concepts that have been covered in this course up to this point.
1. A student receives test scores of 50, 75, and 90. The student’s final exam score is 82 and homework score is 75. Each test is worth 15% of the final grade, the final exam is 35% of the final grade and the homework grade is 20% of the final grade.
a) What is the student’s mean score in the class BEFORE the final exam?
b) What is the student’s mean score in the class AFTER the final exam?
c) Calculate the normal non-weighted average of the 5 grades and compare to the weighted average in part b.
2. The scores for a competency test are approximately symmetric and bell-shaped, with a mean score of 65, with a standard deviation of 4.
a) Can we use the Empirical Rule on this data set? Why?
b) Assuming that we can use the Empirical Rule on this data set, find the percentage of scores between 57 and 73.
c) Provide a statistical argument using your knowledge of the standard deviation to complete this sentence: Most taking this test do not make a score of 77 or above because __________________. (Consider data values outside two standard deviations to be unusual and outside of three standard deviations to be an outlier.)
3. The average SAT verbal score is 490, with a standard deviation of 96.
a) Use the Empirical Rule to determine what percent of the scores lie between 298 and 586.
b) To some, a score of 600 may seem very high compared to the mean of 490. Use the standard deviation to explain why we would not say 600 is unusually high. (Consider data values outside two standard deviations to be unusual and outside of three standard deviations to be an outlier.)
4. Consider the following grades on a test: 98, 51, 94, 67, 94, 73, 75, 89, 22, 99, 84, 89, 87, 93, 81, 92, 71, 61, 10 The mean is 75. Create a stem and leaf display of the data and then answer the following question:
True or False:
a) Most students made C’s.
b) Most students made right around the mean of 75.
c) There was a balanced amount of A’s, B’s, C’s, D’s, and F’s.
d) Half of the grades were below 75 and half above.
Additional discussion topic for this question: When you think of a test average of 75, what automatically comes to your mind about the grades? For most of us, the grades above with an average of 75 does not fit the mold of what we believe an average of 75 means.
