Need Writing Help (stats)

Week 2 Stats

From the list below, choose one problem, write it down, and solve it in detail (show all of your steps). 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.

See the syllabus for complete grading information

4. 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.)

5. 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.)

7. A radio station claims that the amount of advertising per hour of broadcast time is normally distributed with an average of 17 minutes and a standard deviation equal to 2.7 minutes. You listen to the radio station for 1 hour, at a randomly selected time, and carefully observe that the amount of advertising time is equal to 11 minutes.       a) Calculate the z-score for this amount of advertising time.       b) Explain the meaning of this z-score.  Does it mean that 11 is far away from the average of 17 or close to the average of 17?  Would you say that a value of 11 occurs frequently or not (Use Empirical rule to “approximate” a percentage of data values below 11)?  (Consider data values outside two standard deviations to be unusual and outside of three standard deviations to be an outlier.)

10. The mean SAT verbal score is 462, with a standard deviation of 98. Use the Empirical Rule to determine where:

      a) Approximately 95% of the students score. (Assume the data set has a bell-shaped distribution.)

      b) From part a, we can furthermore state that the lowest 2.5% of scores are below ______ and the highest 2.5% of scores are above ________, approximately. 

14. True or False:  After observing the following graph, is it evident that Danielle scored over twice as high as Jared and Alexi?  If false, explain why and how we could correct the graph to not be misleading?  Include a picture of the corrected graph.   

Graph from Fox News