11. Using the empirical rule, 68% of male heights should be between what two values? Either show work or explain how your answer was calculated.
You need the mean (average) and the standard deviation
http://davidmlane.com/hyperstat/z_table.html
The corelation coefficient is: r=0.9982
Step 1: Find X⋅Y, X^ 2 and Y ^2 as it was done in the table below.
X Y X⋅Y X⋅X Y⋅Y
67.273 69.78 4694.30994 4525.656529 4869.2484
0.764 1.40 1.0696 0.583696 1.96
2.533 4.21 10.66393 6.416089 17.7241
63.000 61.00 3843 3969 3721
65.000 67.50 4387.5 4225 4556.25
67.000 71.00 4757 4489 5041
Step 2: Find the sum of every column to get:
¡ÆX=265.57 , ¡ÆY=274.89 , ¡ÆX⋅Y=17693.54347 , ¡ÆX 2 =17215.656314 , ¡ÆY 2 =18207.1825
Step 3: Use the following formula to work out the correlation coefficient.
r = n⋅¡ÆXY−¡ÆX⋅¡ÆY/
[n¡ÆX 2 −(¡ÆX) 2 ]⋅[n¡ÆY 2 −(¡ÆY) 2 ]
¡Ì r = 6⋅17693.54347−265.57⋅274.89/ [6⋅17215.656314−265.57 2 ]⋅[6⋅18207.1825−274.89 2 ]
¡Ì ¡Ö0.9982
Thanks for the help...
Z = -1 to Z = +1
The empirical rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
To find the range of male heights for the 68% statistic, we need to look at one standard deviation from the mean.
First, we need to determine the mean and standard deviation of male heights. Unfortunately, this information was not provided. However, let's assume that the mean height of males is 70 inches with a standard deviation of 3 inches.
To find the range, we can use the following formula:
lower range = mean - 1 * standard deviation
upper range = mean + 1 * standard deviation
lower range = 70 - 1 * 3 = 67 inches
upper range = 70 + 1 * 3 = 73 inches
Therefore, using the empirical rule, approximately 68% of male heights should fall between 67 inches and 73 inches.