Answer:
The cost increase for each square of carpet by 12.
Step-by-step explanation:
The given function is
It is a slope intercept form of the line
Where m is the slope and b is y-intercept.
Therefore the slope of given function is 12 and the y-intercept is 50.
It means the initial ot fixed cost of the carpet is 50 and the cost increased by 12 for each square of carpet.
Answer:
So the value of height that separates the bottom 90% of data from the top 10% is 605.68.
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
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 0.9 of the area on the left and 0.1 of the area on the right it's z=1.28. On this case P(Z<1.28)=0.9 and P(z>1.28)=0.1
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 90% of data from the top 10% is 605.68.