Answer:
x = 25
Step-by-step explanation:
The volume (V) of the triangular prism is calculated as
V = Al ( A is the area of the triangular face and l is its length )
A = bh = 0.5 × 5 × 8 = 20 cm² , then
V = 20 × 20 = 400 cm³
The volume of the cuboid is calculated as
V = lbh = 3.2 × 5 × x = 16x
Given V = 400 cm³ , then
16x = 400 ( divide both sides by 16 )
x = 25
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