19. Write an algebraic expression for the phrase: 6 more than the product of 8 and n.
2 answers:
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Answer:
Horizontal line (0 slope)
Step-by-step explanation:
The equation is , so you'd just insert what you know.
It would look like this: .
We would solve. 6-6=0, while 4-(-2)=6.
So, we have 0/6, which gives you 0, and it would be a horizontal line, since a horizontal line is portrayed by 0 slope.
Answer:
a)
And we can find this probability using the normal standard distribution or excel and we got:
b)
And we can find this probability using the complement rule and normal standard distribution or excel and we got:
c)
And if we solve for a we got
So the value of height that separates the bottom 75% of data from the top 25% is 46.033.
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 heights of a population, and for this case we know the distribution for X is given by:
Where and
Part a
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 using the normal standard distribution or excel and we got:
Part b
And we can find this probability using the complement rule and normal standard distribution or excel and we got:
Part c
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 0.75 of the area on the left and 0.25 of the area on the right it's z=0.674. On this case P(Z<0.674)=0.75 and P(z>0.674)=0.25
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 75% of data from the top 25% is 46.033.