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Luden [163]
3 years ago
9

A commonly used IQ test is scaled to have a mean of 100 and a standard deviation 15. A school counselor was curious about the av

erage IQ of the students in her school and took a random sample of fifty students’ IQ scores. The average of these was 107.9. Find a 95% confidence interval for the student IQ in the school.
Mathematics
1 answer:
Licemer1 [7]3 years ago
4 0

Answer: (103.74,112.06)

Step-by-step explanation:

The confidence interval for population mean is given by :_

\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}

Given : Sample size : n= 50

Sample mean : \overline{x}=107.9

Standard deviation : \sigma=15

Significance level : \alpha: 1-0.95=0.5

Critical value : z_{\alpha/2}=1.96

Then the 95% confidence interval for the student IQ in the school will be :-

107.9\pm (1.96)\dfrac{15}{\sqrt{50}}\\\\\approx107.9\pm0.075\\\\=(107.9-4.16,107.9+4.16)=(103.74,112.06)

Hence, the 95% confidence interval for the student IQ in the school= (103.74,112.06)

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Hi quick whats 18 x 1.25 <br> step by step !!
Ivan

Answer:

22.5

Step-by-step explanation:

125

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2 4

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2. next multiply the 8 by 5 getting 40, drop the 0 anf move the 4 to the top above 2.

3. multiply 8 by 2 getting 16, then add the 4 you have ontop of the 2 to the 16 getting 20. Drop the 0 and bring the 2 over and place it above the one.

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3 years ago
A certain microscope is able to magnify an object up to 100,000 times its original size. In scientific notation, 100,000 is
vova2212 [387]
1.0x10 to the fifth :)
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3 years ago
A parabola intersects the x-axis at x = 3 and x = 9.
Novay_Z [31]

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Solve the system of equations: <br> X+y+z=5<br> -3x-4y+4z=15<br> 2x-y-4z=-8
atroni [7]

Answer:

  (x, y, z) = (3, -2, 4)

Step-by-step explanation:

The attachment shows a solution using a graphing calculator where the first equation is solved for z, and that expression is substituted into each of the other two equations. The solution to that system is (x, y) = (3, -2). Using these values in the expression for z, we find ...

  z = 5 -(3 +(-2)) = 4

The solution is (x, y, z) = (3, -2, 4).

__

Your graphing calculator and/or online tools can give you the reduced row echelon form of the augmented matrix representing the system:

  \left[\begin{array}{ccc|c}1&1&1&5\\-3&-4&4&15\\2&-1&-4&-8\end{array}\right]

__

If you're solving by hand, you can do the substitution described above to eliminate z from one equation. You can eliminate z from another equation by adding the last two:

  -3x -4y +4(5 -x -y) = 15   ⇒   -7x -8y = -5

  (-3x -4y +4z) +(2x -y -4z) = (15) +(-8)   ⇒   -x -5y = 7

This pair of equations can be solved for x and y in any of the usual ways. Using the second equation to substitute for x, for example, gives you ...

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  x = -5(-2) -7 = 3

  z = 5 -(3) -(-2) = 4

_____

<em>Additional comment</em>

If all that is needed is a solution, we prefer a graphical or matrix approach. These take about the same amount of time. Both require a little additional effort to determine exact values when the solutions are not integers.

6 0
2 years ago
Can you please help me thanksss!!!!!!!
Allushta [10]
The correct answer is: H.
4 0
2 years ago
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