A bake sale committee wants to raise $174 for a donation to a local charity. They set aside $12 of their profit at the end of ea
1 answer:
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Answer:
And if we solve for a we got
So the value of height that separates the bottom 95% of data from the top 5% is 251.18.
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 variable of interest of a population, and for this case we know the distribution for X is given by:
Where and
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 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05
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 95% of data from the top 5% is 251.18.
Answer:
Therefore the height of the water in the pool changes at the rate of feet per minute.
Step-by-step explanation:
Given that the shape of swimming pool is right circular cylinder.
The rate of water pouring in the pool = 3 cubic feet per minute.
It means the rate of change of volume is 3 cubic feet per minute.
cubic feet per minute.
When the volume of the swimming pool changed it means the height of the water level of the pool change and the radius of the swimming pool remains constant.
Let the height of the pool be h.
The volume of the pool is = cubic feet
cubic feet
Therefore,
v
Differentiating with respect to t
Putting
The change of height of the pool does not depend on the depth of the pool.
Therefore the rate of change of height of the water in the pool is feet per minute.