Determine where our conception of “freaky fast” (10 minutes) falls on the normal distribution. To do this, draw the normal distribution
For the following questions, you are more than welcome to use a computer (excel) or calculator. Note that the hard part is figuring out what numbers to punch into the calculator/computer. Another note: you do not have to show your work (you can just give a numerical answer where one is asked for). On the other hand, if you show your work, you can get partial credit (maybe you just used the wrong number, but did the actual work right). So, not showing your work means you roll the dice on an all-or-nothing (right or entirely wrong) strategy. Showing your work gives a grey area. This is entirely up to you. Round to the nearest 100th.
- The percentage of high school seniors using alcohol has decreased from 68.2% in 1975 to 52.7% now (2007). What is the absolute change? What is the relative change?
- For the first seven US Presidents, here are their ages when they were inaugurated: 57, 61, 57, 57, 58, 57, 61. For the last seven US Presidents (Ford through Obama), here is the age they were inaugurated: 61, 52, 69, 64, 46, 54, 47. What is the mean, median and mode of each set? What’s the standard deviation of each set? Does the “range rule” work for finding the standard deviation? Are the older group of Presidents older as a group than the younger? Which group shows more variability? Is that remotely relevant to politics?
- Use the Jimmy Johns data we have been collecting and determine the following information for both delivery times (start time and stop time).
JJ1 – a) mean, b) median, c) mode, d) range, e) standard deviation, and f) if “range rule” applies.
JJ2 – Determine if the average delivery is “freaky fast.”
JJ3 – Determine where our conception of “freaky fast” (10 minutes) falls on the normal distribution. To do this, draw the normal distribution noting the mean, +/- 1 standard deviation, +/- 2 standard deviations.
JJ4 – Additionally, find how many standard deviations away from the mean our conception of “freaky fast” falls (what is the z-score for “freaky fast”) and how many standard deviations the max and min fall away from the mean. Then determine what percentile those values are in
JJ5 – Next, look at the rest of the data we collected and develop an explanation for why those deliveries fall so far away from the mean.
JJ6 – Finally, discuss if you think 10 minutes is still “freaky fast” or if you want to revise it to a new time and why.
The data provided is in seconds to make it easier to find the mean, median, mode, and standard deviation but when you draw the normal distribution, you will need to provide your final answers in minutes.
