jadeafrias
24.09.2020 •
Mathematics
Seven less than a number is two
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Ответ:
x-7=2
Step-by-step explanation:
Ответ:
a)
So then we expect aroudn 0.470*10000= 4700 adults scored between 60 and 80.
b)
So the score that separates the bottom 85% of data from the top 15% is 90.6.
c)
So the score that separates the bottom 88% of data from the top 12% is 92.55
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".
Part a
Let X the random variable that represent the variable of interest 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 on this way:
So then we expect aroudn 0.470*10000= 4700 adults scored between 60 and 80.
Part b
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 0.85 of the area on the left and 0.15 of the area on the right it's z=1.04. On this case P(Z<1.04)=0.85 and P(z>1.04)=0.15
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 score that separates the bottom 85% of data from the top 15% is 90.6.
Part c
For this case we want to find a value that satisfy these two conditions:
(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 0.88 of the area on the left and 0.12 of the area on the right it's z=1.17. On this case P(Z<1.17)=0.88 and P(z>1.17)=0.12
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 score that separates the bottom 88% of data from the top 12% is 92.55