There are n gallons of oil. After m gallons have been used then, in terms of m and n, what percent of oil remains? What percent
2 answers:
Answer:
Step-by-step explanation:
Normally wiht number you would just have to do a rile of thirds, but in this case you need to used the values and to think a little outside the box.
YOu knwo that the total number of gallons is "n".
And the used gallons is "m"
To calculate the percentage used you use the next rule of three and clear for "x".
so that would be the expression for gallons used, the remaining gallons expression would be (n-m), so we do the same rule of three but witht the remaining gallons expression:
And that would be the expression for percentage of gallons left.
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Answer:
So the value of height that separates the bottom 10% of data from the top 90% is 30.3.
If the score is lower than 30.3 we consider this score as risk averse
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 scores of a population, and for this case we know the distribution for X is given by:
Where and
We are interested in the bottom 10% of the data.
For this part we want to find a value a, such that we satisfy this condition:
(a)
(b)
Both conditions are equivalent on this case. We can use the z score again in order to find the value a.
As we can see on the figure attached the z value that satisfy the condition with 0.1 of the area on the left and 0.9 of the area on the right it's z=-1.28. On this case P(Z<-1.28)=0.1 and P(z>-1.28)=0.9
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 10% of data from the top 90% is 30.3.
If the score is lower than 30.3 we consider this score as risk averse