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tangare [24]
3 years ago
9

Rachael got a 550 on the analytical portion of the Graduate Record Exam (GRE). If GRE scores are normally distributed and have m

ean μ = 600 and standard deviation σ = 25, what is her standardized score?
Mathematics
1 answer:
valina [46]3 years ago
7 0

Answer:

Z=-2

This value means that the score of Rachel 550 it's 2 deviations below the mean of the population \mu=600

Step-by-step explanation:

1) 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".  

\mu=600 represent the population mean for the Graduate Record Exam (GRE)

\sigma=25 represent the population standard deviation for Graduate Record Exam (GRE)

2) Solution to the problem

Let X the random variable that represent the Graduate Record Exam (GRE) of a population, and for this case we know the distribution for X is given by:

X \sim N(600,25)  

Where \mu=600 and \sigma=25

We want to find the z score for a score of 550. And in order to do this we need to apply the formula for the z score given by:

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

If we apply this formula to our probability we got this:

z=\frac{550-600}{25}=-2

So the answer for our case would be Z=-2

This value means that the score of Rachel 550 it's 2 deviations below the mean of the population \mu=600

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Answer:

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Step-by-step explanation:

Let's say that the first number is x and the second one is y.

First, the difference between them is 7, so x-y=7

Next, the sum of their squares is 949, so x²+y² = 949

We have

x-y=7

x²+y²=949

One thing we can do to solve this problem is to solve for x in the first equation, plug that into the second equation, and go from there

Adding y to both sides in the first equation, we have

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Plugging that into the second equation for x, we have

(7+y)²+ y² = 949

expand

(7+y)(7+y) + y² = 949

49 + y² + 7y + 7y + y² = 949

combine like terms

2y² +14y + 49 = 949

subtract 949 from both sides to put this in the form of a quadratic equation

2y² + 14y - 900 = 0

divide both sides by 2

y² + 7y - 450 = 0

To factor this, we want to find 2 numbers that add up to 7 and multiply to -450.

The factors of 450 are as follows:

1, 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, 225, and 450.

Note that we want to find two numbers with a difference of 7, as one will have to be negative for the multiplication to end up at -450. Two numbers that stand out are 18 and 25. To make them add up to 7, 18 can be negative. We therefore have

y² + 25y - 18y - 450 = 0

y(y+25) - 18(y+25) = 0

(y-18)(y+25) = 0

Solving for 0,

y-18 = 0

add 18 to both sides

y=18

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subtract 25 from both sides

y= -25

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x-18 = 7

add 18 to both sides to isolate x

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Example

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