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Helga [31]
3 years ago
6

The weight of baby goats is believed to be Normally distributed, with a mean of 5.75 pounds. The average weight of a random samp

le of 20 baby goats is found to be 6.15 pounds, with a standard deviation of 0.35 pound. What is the standard error of the mean
Mathematics
1 answer:
Julli [10]3 years ago
7 0

Answer:

The standard error of the mean is 0.0783.

Step-by-step explanation:

The Central Limit Theorem helps us find the standard error of the mean:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

The standard deviation of the sample is the same as the standard error of the mean. So

SE_{M} = \frac{\sigma}{\sqrt{n}}

In this problem, we have that:

\sigma = 0.35, n = 20

So

SE_{M} = \frac{\sigma}{\sqrt{n}}

SE_{M} = \frac{0.35}{\sqrt{20}}

SE_{M} = 0.0783

The standard error of the mean is 0.0783.

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Answer:

4.32

Step-by-step explanation:

You can multiply 16 by 0.27 to get the answer.

16*0.27=4.32

You can check your work with estimation because 27% is about 1/4 of the number, and just by looking at the number, 4 is 1/4 of the number.

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2 years ago
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            Find the approximate solution of this system of equations.
Montano1993 [528]
Y = |x² - 3x + 1|
y = x - 1

|x² - 3x + 1| = x - 1
|x² - 3x + 1| = ±1(x - 1)
|x² - 3x + 1| = 1(x - 1)       or      |x² - 3x + 1| = -1(x - 1)
|x² - 3x + 1| = 1(x) - 1(1)    or    |x² - 3x + 1| = -1(x) + 1(1)
|x² - 3x + 1| = x - 1        or         |x² - 3x + 1| = -x + 1
  x² - 3x + 1 = x - 1         or          x² - 3x + 1 = -x + 1
        - x        - x                                + x         + x
  x² - 4x + 1 = -1           or            x² - 2x + 1 = 1
              + 1 + 1                                       - 1 - 1
  x² - 4x + 1 = 0              or           x² - 2x + 0 = 0
  x = -(-4) ± √((-4)² - 4(1)(1))    or    x = -(-2) ± √((-2)² - 4(1)(0))
                      2(1)                                             2(1)
  x = 4 ± √(16 - 4)            or            x = 2 ± √(4 - 0)
                 2                                                 2
  x = 4 ± √(12)              or               x = 2 ± √(4)
             2                                                  2
 x = 4 ± 2√(3)               or               x = 2 ± 2
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 x = 2 + √(3)  or  x = 2 - √(3)   or    x = 1 + 1    or    x = 1 - 1
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y = x - 1          or           y = x - 1                            or    y = x - 1   or    y = x - 1
y = (2 + √(3)) - 1    or    y = (2 - √(3)) - 1          or         y = 2 - 1    or    y = 0 - 1
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The solution (0, -1) can be made by one function (y = x - 1) while the solution (2 ± √(3), 1 ± √(3)) can be made by another function (y = |x² - 3x + 1|). So the solution (2, 1) can be made by both functions, making the two solutions equal.
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How to solve the inequality
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Answer:

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Step-by-step explanation:

1. Multiply both sides by 6 (the LCM of 6,3)

5/2 + 3-x <= 2(x-2)

2. Simplify 5/2+3-x to 11/2-x

11/2 - x<=2 (x-2)

3. Expand.

11/2-x<= 2x-4

4. Add x to both sides.

11/2<= 2x-4+x

5. Simplify 2x-4+x to 3x-4.

11/2<=3x-4

6. Add 4 to both sides.

11/2+4<=3x

7. Simplify 11/2+4 to 19/2

19/2<=3x

8. Divide both sides by 3

19/2 /3 <=x

9. Simplify 19/2 /3 to 19/2*3

19/2*3<=x

10. Simplify 2*3 to 6

19/6<=x

11. Switch sides.

x>= 19/6

Hope this helps!

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Answer:

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2) The value of y according to the regression line is 19.2.

3) The residual is the difference between the value from the regression line and the real value. In this case, the residual value is 0.

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Sveta_85 [38]
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