abbygriffin2009
12.09.2019 •
Mathematics
The heights of men in the united states are approximately normally distributed with mean 69.1 inches and standard deviation 2.9 inches. the heights of women in the united states are approximately nor- mally distributed with mean 63.7 inches and standard deviation 2.7 inches. additionally, suppose that the heights of husbands and wives have a correlation of 0.3. let x and y be the heights of a married couple chosen at random. what are the mean and standard deviation of the average height,
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Ответ:
Step-by-step explanation:
Let M be the heights of men in the United States and W be the heights of women in the United States
Given that M is N(69.1, 2.9) and W (63.7, 2.7)
For a husband and wife we have average height as
Var (Z) =![Var (\frac{x+y}{2} )=\frac{1}{4}[Var(x)+ Var(y)+2 cov (x,y)]\\](/tpl/images/0229/3179/eb7b2.png)
=![0.25[2.9^2+2.7^2+2*r*sx*sy]\\= 0.25(20.398)\\=5.0995](/tpl/images/0229/3179/2059c.png)
Mean = 66.4" and std dev = 2.258
Ответ:
a = 0.24
Plug it in our equation:
2(0.24) + 3p = 1.59
Multiply:
0.48 + 3p = 1.59
Subtract 0.48 to both sides:
3p = 1.11
Divide 3 to both sides:
p = 0.37
So one pair costs £0.37