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GuDViN [60]
3 years ago
9

Joses ACT score had a z-score of .75.what was his ACT score? mean score=21.1 sd=5.2

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
6 0

Answer:

X \sim N(21.1,5.2)  

Where \mu=21.1 and \sigma=5.2

And the z score is given by:

z = \frac{x -\mu}{\sigma}

And since z = 0.75 we can replace like this:

0.75 = \frac{x- 21.1}{5.2}

And if we solve for x we got:

x = 21.1 +0.75*5.2 = 25

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 ACT scores of a population, and for this case we know the distribution for X is given by:

X \sim N(21.1,5.2)  

Where \mu=21.1 and \sigma=5.2

And the z score is given by:

z = \frac{x -\mu}{\sigma}

And since z = 0.75 we can replace like this:

0.75 = \frac{x- 21.1}{5.2}

And if we solve for x we got:

x = 21.1 +0.75*5.2 = 25

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The shape of the normal distribution is bell shape and it is also symmetrical from the left and right sides about the origins (mean).

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A normal distribution is a function on some random variables, which represent the set of all those random variables in a symmetrical bell shape about the mean value.

It shows that the probability of occurrence of some data which is distributed over a function is more at or around the mean.

It is also known as probability distribution curve.

The normal distribution has two parameters:

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What is the shape of the normal distribution?

The normal distribution curve is at it's peak at the mean value. This shows that the probability of occurrence of the data or value is more concentrated or distributed about the mean. It is also symmetric about the mean. As we more further from the mean, we see that the normal distribution curve gradually decreases showing that the probability of occurrence of the data or the values decreases. The shape that this curve forms is like a bell-shaped. So the shape of normal distribution is bell shape.

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Know more about "normal distribution" here: brainly.com/question/15103234

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5 0
1 year ago
Julien's parents want $64,000 at the end of 3 years. They put their money in an account that yields 10% per year compounded mont
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Answer: \$47,471

Step-by-step explanation:

Given

Julien's parents want $64,000 at the end of 3 years

The rate of interest is 10% annually

Suppose they invested P amount initially

So, compound interest, compounded monthly is

\Rightarrow A=P\left( 1+\frac{r}{n}\right)^{nt}\quad [\text{n=Numner of compounding periods}]\\\\\text{Insert the values}\\\Rightarrow 64,000=P\left( 1+\frac{0.10}{12}\right)^{12\times 3}\\\\\Rightarrow 64,000=P\left( 1+\frac{10}{12}\right)^{36}\\\\\Rightarrow P=\dfrac{64000}{1.3481}\\\\\Rightarrow P=\$\ 47,471.37\approx \$ 47,471

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What is down payment with regard to buying a house?
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3 years ago
The land area of a country is about 5.0 million square​ miles, and the population is about 600 million people. What is the avera
podryga [215]

Answer:

120 people/sq. mile

Step-by-step explanation:

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The population density is found by dividing the "number of people" by the "land area" (in sq mile or sq km).

Here, it is given there are 600 million people, so

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6 0
3 years ago
How many solutions does the system have?
amid [387]

Answer:

A; infinitely many solutions

Step-by-step explanation:

first, let's simplify the first equation to make it simpler.

divide both sides by 5

y=3x-8

new system

y=3x-8

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as you can see, they are the same.

not mandatory but useful!⬇⬇⬇⬇

just to be more clear, let's substitute them. since they're both already in y=, we can make them both set to each other.

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add 8 to both sides; subtract 3x from one side

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the answer is A, Infinitely many solutions.

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