Mathematical models are used as tools to describe reality. These models are supposed to characterize the important features of the analyzed phenomena and provide insight. The normal distribution is an example of a random variable that is widely used by researchers to model real data.
Researchers often model real observations using the normal distribution, but sometimes the real distribution is a bit different from the perfect, normal distribution. List some reasons why researchers might make approximations like this and describe at least one situation when researchers should not use this approximation.
When forming your answer to this question you may give an example of a situation from your own field of interest for which a random variable can serve as a model.

There are several reasons why researchers might not use the normal distribution to model real data which are due to assumptions of normal distribution.

First, the normal distribution assumes that the data is symmetric and is distributed around the mean. However, in some cases, the data may be skewed, making the normal distribution an inappropriate model.

Second, the normal distribution assumes that the data is homoscedastic, meaning that the variance is constant across the sample. However, in some cases, the variance may be heteroscedastic, meaning that the variance changes across the sample. This makes the normal distribution an inappropriate model for this type of data.

One situation in which researchers should not use the normal distribution approximation is when modeling financial data. Financial data often follows a power-law distribution, which is not normal. Therefore, researchers should use a power-law distribution to model this type of data.

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Solve the equation for the value of x,
-4x=36

Please show your work, thank you.

if the nth term of a number sequence is n squared-3 if the first 3 terms and the 10th term

Which is equivalent to the series shown?
12
Which expansion is equivalent to the summation
shown?
12
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20 9+10 +11+12+
9 10 11 12
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12 12
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12 + 20
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1 1 1
9+10+11+12+ 20
9 10 11 12
20Σ
COMPLETE
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Intro
Final

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This is an isosceles trapezoid.
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Enter the number that belongs in
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Select the name of the highlighted part.
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Evaluate \frac{1}{4} \times 2 \frac{4}{5}
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Write the answer as a reduced fraction.​

​Use slash \left(/\right)(/) to separate numerator and denominator.

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Anya bought some cans of paint. She used 9 of them to
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A culture of bacteria has an initial population of 89000 bacteria and doubles every 8 hours. Using the formula P_t = P_0\cdot 2^{\frac{t}{d}}P t ​ =P 0 ​ ⋅2 d t ​ , where P_tP t ​ is the population after t hours, P_0P 0 ​ is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 11 hours, to the nearest whole number?

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The following data set shows the number of project points each student in a class earned last week.
68, 84, 86, 74, 58, 82, 82, 96, 78, 96, 70, 78, 98, 80, 94, 96, 64, 82, 74, 78, 96. W
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find the length of the side x in simplest form with a rational denominator.
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divide the polynomial (x^2 + 3x + 5) by 2x + 1​

A local artisan makes handmade ceramic vases and bowls. Each vase takes 3 hours to make and each bowl takes 2 hours to make. He is limited to at most 30 hours of work time a week and would like to produce at least 12 items weekly.

Write a system of inequalities that represents the situation.
Group of answer choices

3v + 2b ≤ 30
3v + 2b ≥ 12

3v + 2b ≥30
v + b ≤ 12

2v + 3b ≤ 30
v + b ≥12

3v + 2b ≤ 30
v + b ≥ 12