e. Use the table below to determine the following: Height Z-Score -3 61.5 -2 64 -1 66.5 69 1 71.5 2 74 3 76.5 If there are approximately 152 million adult American men in the United States, how many of them do you expect to be between 69 and 71.5 inches tall? million American men.
e. Use the table below to determine the following: Height Z-Score -3 61.5 -2 64 -1 66.5 69 1 71.5 2 74 3 76.5 If there are approximately 152 million adult American men in the United States, how many of them do you expect to be between 69 and 71.5 inches tall? million American men.
e. Use the table below to determine the following: Height Z-Score -3 61.5 -2 64 -1 66.5 69 1 71.5 2 74 3 76.5 If there are approximately 152 million adult American men in the United States, how many of them do you expect to be between 69 and 71.5 inches tall? million American men.
The Normal DistributionThe Normal Distribution is a Continuous Probability Distribution that is commonly applied when there is a "common" value among data while more extreme values are less likely. The characteristics of the Normal Distribution are:
The mean, median, and mode are are equal (or nearly equal).
The curve is symmetric at the center.
Half of the values are to the left of the center (mean) and the other half are to the right
The total area under the curve is 1.
Applying the Normal Distribution to a scenario. The distribution of heights of adult American men (in inches) is apporximately normal such that X∼N(69,2.5)X∼N(69,2.5).
Use the scenario above to determine the selected probabilities below. You may wish to use the Normal Distribution Calculator hosted by the University of Iowa's Department of Mathematical Sciences. Remember: the formatting of this calculator may vary slightly from what is used in class. (link: Normal Distribution Calculator) (Include four decimal places in your answers below.)
Transcribed Image Text:e. Use the table below to determine the following:
Height
Z-Score
-3
61.5
-2
64
-1
66.5
69
1
71.5
2
74
3
76.5
If there are approximately 152 million adult American men in the United States, how many of them
do you expect to be between 69 and 71.5 inches tall?
million American men.
Definition Definition Measure of central tendency that is the value that occurs most frequently in a data set. A data set may have more than one mode if multiple categories repeat an equal number of times. For example, in a data set with five item—3, 5, 5, 29, 473—the mode is 5 because it occurs twice and no other value occurs more than once. On a histogram or bar chart, the element with the highest bar represents the mode. Therefore, the mode is sometimes considered the most popular option. The mode is useful for nominal or categorical data (e.g., the most common color car that users purchase), but it is problematic for continuous data because it is more likely not to have any value that is more frequent than the other.
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