The graph of a function f(x) is shown below: What is the domain of f(x)?

The sum of two numbers is 136. One number is 51. What is other? What are the common factors of these two numbers?

Vsevolod [243]

75 // common factor is 3

8 0

3 years ago

Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, port

GrogVix [38]

Answer:

$a=49.5 -1.28*15=30.3$

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:

$X \sim N(49.5,15)$

Where $\mu=49.5$ and $\sigma=15$

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:

$P(X>a)=0.9$ (a)

$P(X$ (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:

$P(X$