What is 1,248 divided by 24?
2 answers:
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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
Answer:
0.70275
Step-by-step explanation:
Data provided in the question:
4e²ˣ⁻¹ -1 = 5
now solving for 'x'
⇒ 4e²ˣ⁻¹ = 5 + 1
or
⇒ 4e²ˣ⁻¹ = 6
or
⇒
or
⇒
now,
taking natural log both sides, we get
⇒ 2x - 1 =
also,
we know
⇒
thus,
⇒ 2x - 1 = ln(3) - ln(2)
or
⇒ 2x - 1 = 1.0986 - 0.6931
or
⇒ 2x - 1 = 0.4055
or
⇒ 2x = 0.4055 + 1
or
⇒ 2x = 1.4055
or
⇒ x = 0.70275