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tester [92]
2 years ago
7

The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard devi

ation of 100.
Using the empirical rule, what is the probability that a randomly selected student’s math score is between 300 and 700? Express your answer as a decimal.
Mathematics
2 answers:
s2008m [1.1K]2 years ago
6 0
I this the answer you are looking for would probably be 47.7%. hope this helps!!
egoroff_w [7]2 years ago
6 0

Answer:

The probability that a randomly selected student’s math score is between 300 and 700 is 0.9544.

Step-by-step explanation:

We have given that, The SAT mathematics scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard deviation of 100.

To find : What is the probability that a randomly selected student’s math score is between 300 and 700?

Solution :

The mean is \mu=500

The standard deviation is  \sigma=1000

Formula to find z-score is

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

Now, we have to find the probability score is between 300 and 700              

For x = 300 substitute in the formula,

z = \frac{300-500}{100}\\\\z =-2

For x = 700 substitute in the formula,

z = \frac{700-500}{100}\\\\z =2

Now, The probability between P(-2<z<2)  is written as

P(-2

Using the z table substitute the values of z

At z<-2 is 0.228 and at z<2 is 0.9772.

P(-2

P(-2

Therefore, The probability that a randomly selected student’s math score is between 300 and 700 is 0.9544.

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The equation of a circle whose centre (-5,-2) and radius 2 is x^{2}+y^{2}+10x+4y+25=0

What is equation of a circle?

A circle is a closed curve drawn from a fixed point called centre of the circle. The distance between the centre of the circle and the arc of the circle is called the radius of the circle.

The equation of a circle with centre (h, k) radius r is

(x-h)^{2} +(y-k)^{2}=r^{2}

Given center = (-5,-2)  and Radius = 2

Put the Given value in the equation:

= (x-(-5))^{2} +(y-(-2))^{2} = 2^{2}

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= (x^{2} +10x+25)+(y^{2}+4y+4)= 4

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So, the equation of the circle whose centre is (-5,-2) and Radius 2 is

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