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KengaRu [80]
2 years ago
5

A college conducts a common test for all the students. For the Mathematics portion of this test, the scores are normally distrib

uted with a mean of 502 and a standard deviation of 115. Based on this information, what percentage of students would be expected to score between 400 and 590
Mathematics
1 answer:
Jet001 [13]2 years ago
6 0

Using the normal distribution, it is found that 58.97% of students would be expected to score between 400 and 590.

<h3>Normal Probability Distribution</h3>

The z-score of a measure X of a normally distributed variable with mean \mu and standard deviation \sigma is given by:

Z = \frac{X - \mu}{\sigma}

  • The z-score measures how many standard deviations the measure is above or below the mean.
  • Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

\mu = 502, \sigma = 115

The proportion of students between 400 and 590 is the <u>p-value of Z when X = 590 subtracted by the p-value of Z when X = 400</u>, hence:

X = 590:

Z = \frac{X - \mu}{\sigma}

Z = \frac{590 - 502}{115}

Z = 0.76

Z = 0.76 has a p-value of 0.7764.

X = 400:

Z = \frac{X - \mu}{\sigma}

Z = \frac{400 - 502}{115}

Z = -0.89

Z = -0.89 has a p-value of 0.1867.

0.7764 - 0.1867 = 0.5897 = 58.97%.

58.97% of students would be expected to score between 400 and 590.

More can be learned about the normal distribution at brainly.com/question/27643290

#SPJ1

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Paul [167]

Remark

I'll do two from each group, leaving you with 1. I just leave the answer for the one I don't do or a hint it it is long. That's more than we are instructed to do (which is three parts per posted question).

One

Two ratios form a proportion because they both equal the same thing when you reduce them to the point where the ratios are prime to each other.

3/4 = 12/16

3/4 can't be reduced any further. When both 12 and 16 are divided by 4, the result is 3/4

Two

<em><u>Formula</u></em>

Sale Price/Original Price = 3/4

<em><u>Solve</u></em>

Sale Price / 64 = 3/4           Multiply both sides by 64

Sale Price = (3/4)*64

Sale Price = 48

Three

682 Trillion atoms of hydrogen.

Four

<em><u>Formula</u></em>

rotations / 40 seconds = rotations / second

<em><u>Solve</u></em>

2000 / 40 seconds = rotations / 1 second    Just divide

50 rotations/1 second = rotations / second.

Five

<em><u>Formula</u></em>

Herd of cows / Total pounds of milk = 1 cow / pounds of milk

<em><u>Given</u></em>

Herd = 12

pounds total = 224998

<em><u>Solve</u></em>

12/224998 = 1 / x             Cross multiply

12x = 224998

x = 18750 pounds of milk for 1 cow.

Six

0.5 m in 1 second.

Seven

<em><u>Formula</u></em>

Pages / hour = pages / minute

pages / hour = 4.5

1 hour = 60 minutes.

<em><u>Solve</u></em>

4.5 / 1 hour. But 1 hour = 60 min

4.5 pages / 60 min = 0.075 pages per minute.

Note this is not a true proportion. You just have to know how it is done.

Eight

This is also not a true proportion. The best way to do this is called unit analysis.

\dfrac{18feet}{2seconds} * \dfrac{1 mile}{5280 feet}\dfrac{3600sec}{1hour}

Each set of units on the right will cancel with a set of units on the left until all that you area left with is miles / hour. Then just multiply the numerator numbers together and denominator numbers together.

numerator: 18 * 1 * 3600 = 64800

denominator: 2 * 5280 * 1 = 10560

Now divide the numerator by the denominator.

answer: numerator/denominator = 64800/10560 = 6.14 miles per hour.

Nine                                              

Note: there are 1760 yards in a mile.

1 gallon will take you 32000 yards or 18 miles. Do this the same way eight was done.

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3 years ago
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I need to know the whole process of this equation
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8 0
3 years ago
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mr Goodwill [35]

Answer:When planning your writing, it is important to consider the best way to communicate information to your audience, especially if you plan to use data in the form of numbers, words, or images that will help you construct and support your argument.  Generally speaking, data summaries may take the form of text, tables or figures. Most writers are familiar with textual data summaries and this is often the best way to communicate simple results. A good rule of thumb is to see if you can present your results clearly in a sentence or two. If so, a table or figure is probably unnecessary. If your data are too numerous or complicated to be described adequately in this amount of space, figures and tables can be effective ways of conveying lots of information without cluttering up your text. Additionally, they serve as quick references for your reader and can reveal trends, patterns, or relationships that might otherwise be difficult to grasp.

So what’s the difference between a table and a figure anyway?

Tables present lists of numbers or text in columns and can be used to synthesize existing literature, to explain variables, or to present the wording of survey questions. They are also used to make a paper or article more readable by removing numeric or listed data from the text. Tables are typically used to present raw data, not when you want to show a relationship between variables.

Figures are visual presentations of results. They come in the form of graphs, charts, drawings, photos, or maps.  Figures provide visual impact and can effectively communicate your primary finding. Traditionally, they are used to display trends and patterns of relationship, but they can also be used to communicate processes or display complicated data simply.  Figures should not duplicate the same information found in tables and vice versa.

Using tables

Tables are easily constructed using your word processor’s table function or a spread sheet program such as Excel. Elements of a table include the Legend or Title, Column Titles, and the Table Body (quantitative or qualitative data). They may also include subheadings and footnotes. Remember that it is just as important to think about the organization of tables as it is to think about the organization of paragraphs. A well-organized table allows readers to grasp the meaning of the data presented with ease, while a disorganized one will leave the reader confused about the data itself, or the significance of the data.

Title: Tables are headed by a number followed by a clear, descriptive title or caption. Conventions regarding title length and content vary by discipline. In the hard sciences, a lengthy explanation of table contents may be acceptable. In other disciplines, titles should be descriptive but short, and any explanation or interpretation of data should take place in the text. Be sure to look up examples from published papers within your discipline that you can use as a model. It may also help to think of the title as the “topic sentence” of the table—it tells the reader what the table is about and how it’s organized. Tables are read from the top down, so titles go above the body of the table and are left-justified.

Column titles: The goal of column headings is to simplify and clarify the table, allowing the reader to understand the components of the table quickly. Therefore, column titles should be brief and descriptive and should include units of analysis.

Table body: This is where your data are located, whether they are numerical or textual. Again, organize your table in a way that helps the reader understand the significance of the data. Be sure to think about what you want your readers to compare, and put that information in the column (up and down) rather than in the row (across). In other words, construct your table so that like elements read down, not across. When using numerical data with decimals, make sure that the decimal points line up. Whole numbers should line up on the right.

Other table elements

Tables should be labeled with a number preceding the table title; tables and figures are labeled independently of one another. Tables should also have lines demarcating different parts of the table (title, column headers, data, and footnotes if present). Gridlines or boxes should not be included in printed versions. Tables may or may not include other elements, such as subheadings or footnotes.

Quick reference for tables

Tables should be:

Centered on the page.

Numbered in the order they appear in the text.

Referenced in the order they appear in the text.

Labeled with the table number and descriptive title above the table.

Labeled with column a

Step-by-step explanation:

8 0
3 years ago
mr.lumen replaced a square window with a rectangular one.The new window is 3 ft wider and 2 ft higher than the square one.it has
stira [4]

Alright, lets get started.

Suppose the original square window has the side = x feet

The new window is 3 ft wider and 2 ft higher than the square one.

Means length of the new window will be = (x+3)

Width of the new window will be = (x+2)

So the area of the new window will be = (x+3)(x+2)

So the area of the new window will be = x^2 + 2x + 3x + 6

So the area of the new window will be = x^2 + 5x + 6

As given in question the area of 30 square feet for the new window, hence

x^2 + 5x + 6 = 30

x^2 + 5x - 24 = 0

Factoring

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x = -8 or x = 3

Side could not be negative hence

side of the original square window will be = 3 feet : Answer

Hope it will help :)

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3 years ago
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frutty [35]

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Hope this helps.

8 0
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