Solve the proportion/percent problem:
1 answer:
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Answer:
And if we solve for a we got
And the limits for this case are: (214.4; 295.4)
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 annual precipitation of a population, and for this case we know the distribution for X is given by:
Where and
The confidence level is 95.44 and the signficance is and the value of
. And the critical value for this case is
Using this condition we can find the limits
And if we solve for a we got
And the limits for this case are: (214.4; 295.4)
Height of the water increasing is at rate of
With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:
There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:
Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:
In the problem, we are given
So we need to substitute this in:
Hence, Height of the water increasing is at rate of
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