Answer:
And we can find this probability using the normal standard table or excel:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Solution to the problem
Let X the random variable that represent the amount of ml of a population, and for this case we know the distribution for X is given by:
Where
and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability using the normal standard table or excel:
Answer:
x = 12
Step-by-step explanation:
In a right triangle (a triangle that has a ninety degree angle in it) the the square of the side opposite the right angle is always equal to the sum of the squares of the other two sides. Therefore, we can use the information we are given to figure out the missing side:
![15^2=225\\9^2=81\\225-81=144\\\sqrt[2]{144}=12](https://tex.z-dn.net/?f=15%5E2%3D225%5C%5C9%5E2%3D81%5C%5C225-81%3D144%5C%5C%5Csqrt%5B2%5D%7B144%7D%3D12)
In order to solve the amount of each solution, we need to set up equations. We do as follows:
Let x = solution with 32% sodium
y = solution with 12% sodium
Overall balance
x + y = 50
Component balance
.32x + .12y = 50(.20) =10
Solving simultaneously,
x = 20
y = 30
Hope this answers the question. Have a nice day.