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lys-0071 [83]
3 years ago
12

Suppose the area of a circle with radius r r is larger than the area of a square with side length l l . define a formula that ex

presses d d, how much greater the area of a circle with radius r r is than the area of a square with side length l l , in terms of r r and l l . (that is, write a formula that expresses d d in terms of r r and l l .)
Mathematics
1 answer:
lawyer [7]3 years ago
3 0
We know that the area of any circle is  Ac = πr**2The area of the square is As = l**2 
If we substract the Areas, we can know the difference between them

d = πr**2 - l**2
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Answer:

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So then is appropiate use the normal distribution to find the probabilities for \bar X

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".  The letter \phi(b) is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: \phi(b)=P(z

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:

X \sim N(61,14)  

Where \mu=61 and \sigma=14

Since the distribution for X is normal then the distribution for the sample mean \bar X is also normal and given by:

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\mu_{\bar X} = 61

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