Discussion Question 3: Normal and non-Normal data The Normal distribution is a v
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Question
Discussion Question 3: Normal and non-Normal data
The Normal distribution is a very important density curve. It is symmetric around a single peak. Table A on pages 698 and 699 of the text gives us the areas under regions of the Normal distribution curve. Many data sets drawn from nature follow the Normal curve and as we go through the course we will see the Normal
12 ACTIVITIES AND ASSIGNMENTS FOR WEEK 2 curve show up in another important application. Not all data sets follow this distribution, though. Let’s try to build up some intuition about density curves by trying to distinguish between the types of data that will have a Normal distribution and the types that will likely be non-Normal. [Note that when referring to this special distribution we will capitalize the word Normal to distinguish it from the common English word normal, meaning standard, usual, or commonplace.] Several hypothetical sets of data are described below. Identify one data set that is likely to have a Normal distribution (or approximately Normal) and one that is likely to be non-Normal. Describe how you think the non-Normal data set will differ from being normally distributed. (Will the data set be symmetric? skewed? bimodal?) Make a rough sketch of a possible density curve for this data set and post it in your reply. (Please only answer one part at a time to give other students a chance to answer as well! Start with the first one!) I am looking to do number 3 and 4 for this question.
(1) The dates found on the pennies in all the cash drawers in the Wal-Mart in north Raleigh, NC.
(2) The annual income of every adult resident of Omaha, NE.
(3) The heights of the mature redwood trees in Redwood National Park.
(4) The ages of death of individuals buried in a medieval cemetery in southern France.
(5) The annual rainfall on top of Devil’s Tower, Wyoming for each of the past 250 years.
(6) The shoe size of every pair of women’s shoes sold last year at the Foot Locker in the Mall of America.
(7) The model year of every car registered in Pasadena, CA.
(8) The number of traffic accidents experienced by each resident of Boulder City, CO.
(9) The SAT scores of all seniors in the class of 2011.
(10) The weights of each egg laid by the hens in my fiancee’s parents’ backyard chicken coop for a year.
(Let’s say all the hens are exactly the same species.)
(11) The four-digit numbers found on New York State license plates issued in 2010.
(12) The birth weights of blue whales born during the past decade.
(13) The ages of students at Utica College.
(14) The gross domestic product of all countries in the world.
(15) The actual volumes of all Enfamil baby formula of a specific size made by a factory in one month.
Can you detect a common theme or themes among the data sets that are Normally distributed? What
kinds of data sets are likely to be Normal or approximately Normal?
Explanation / Answer
3) let X be the random variable denoting height of trees in park.
Here note that X has distribution of height that is continuous.
Also X has mean M and Variance is S
Also in real scenario it can be seen that height of M trees are has higher frequency. Below or above of M has low frequency of height.
So here we can assume a bell shaped distribution of X, that is Normal Distribution.
X~N(M, S)
4) Let Y be a random variable denoting age of the dead person.
Y is also continously distributed having mean M and Variance S,
In the same argument as 3, we can say that Y~N(M, S)