9514 1404 393
Answer:
y-4 = -2(x+1)
Step-by-step explanation:
The point-slope equation of a line is ...
y -k = m(x -h) . . . . . line with slope m through point (h, k)
You have m = -2 and (h, k) = (-1, 4). Putting these numbers into the above form gives ...
y -4 = -2(x +1)
The probability would be 0.1971.
We will calculate a z-score for each end of this interval.
z = (X-μ)/σ
For the lower limit:
z = (1100-1050)/218 = 50/218 = 0.23
For the upper limit:
z = (1225-1050)/218 = 175/218 = 0.80
Using a z-table (http://www.z-table.com) we see that the area under the curve to the left of, less than, the lower limit is 0.5910. The area under the curve to the left of, less than, the upper limit is 0.7881. To find the area between them, we subtract:
0.7881 - 0.5910 = 0.1971
Answer:
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.
Step-by-step explanation:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
Where 
and 
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842
If we use condition (b) from previous we have this:
But we know which value of z satisfy the previous equation so then we can do this:
And if we solve for a we got
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.
The line segment HI has length 3<em>x</em> - 5, and IJ has length <em>x</em> - 1.
We're told that HJ has length 7<em>x</em> - 27.
The segment HJ is made up by connecting the segments HI and IJ, so the length of HJ is equal to the sum of the lengths of HI and IJ.
This means we have
7<em>x</em> - 27 = (3<em>x</em> - 5) + (<em>x</em> - 1)
Solve for <em>x</em> :
7<em>x</em> - 27 = (3<em>x</em> + <em>x</em>) + (-5 - 1)
7<em>x</em> - 27 = 4<em>x</em> - 6
7<em>x</em> - 4<em>x</em> = 27 - 6
3<em>x</em> = 21
<em>x</em> = 21/3
<em>x</em> = 7
