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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using the figure below complete the proof. Which of the following sequence of reasons may be used to fill the blanks in the two-columns proof above?

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

divide the polynomial (x^2 + 3x + 5) by 2x + 1​

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Anya bought some cans of paint. She used 9 of them to
paint the house and had 23 left. Write an equation, that
when solved, will tell how many cans of paint, p, that Anya
bought?

Find the mean of these numbers: 8, 14, 32, 6, 15

the other answer choice is 75​

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
Which dot plot correctly displays this data?

Two equilateral triangle’s are showing. Find the scale factor used on the first triangle to make the second triangle

if Mike Burns 220 calories in 20 minutes and 275 calories is in 25 minutes 385 calories in 35 minutes how much calories did he burn in 29 minutes​

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?

find the volume of the cone. make sure to round

If p varies jointly as q and r, and p = 150 when q = 18 and r = 5, find q when p = 345 and r = 9.​

Below, the two-way table is given for a class of students. Juniors Seniors Free Freshmen Sophomore Male 4 6 2 2. Female 3 4 6 3 Total If a student is selected at random, find the probability the student is a junior given that it's male. Round to the nearest whole percent.​

What is the area of triangle HGF? Round your answer to the nearest tenth of a square centimeter. Recall that you need to round up if the value of the hundredth is 5 or greater?

Abigail wants to ride her bicycle 37 miles this week. She has already ridden 17 miles. If she rides for 5 more days, what is the average number of miles she would have to ride each day to meet her goal? Need help for delta math

find the length of the side x in simplest form with a rational denominator.
i need help understanding these type of questions pls​

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

Please show your work, thank you.

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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what are the answers?

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

QRST is an isosceles trapezoid and m

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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

Given the function f(x) = 5x2 - 3x + 2, what is f(2)?

Select the name of the highlighted part.
OA side
OB. diagonal
OC.
Vertex

Can someone help me please with three questions? 31, 35 and 37?

Find x if x + y = 16, x * 3 is even, x is a factor of y, and 2x+y= 20.

Find f(3.5) if f(x) = (4x - 2)/10

ext year, my age will be 125% more than it was when I got married. I got married when I was 24. How old will I be next year?

If 14 g of a radioactive substance are present initially and 3 yr later only 7 g​ remain, how much of the substance will be present after 6 ​yr?