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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

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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Here , we are provided with a table which shows 5 consecutive terms of an arithmetic sequence . But before solving further , let's recall that ;

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Now , here we are given with ;

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We have to find the 2nd , 3rd and 4th term respectively ,

Now , by using the above formula , 5th term can be written as ;

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Putting the values and transposing 1st term to RHS , we have ;

${: \implies \quad \sf 4d = -4-8}$

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Now , as we got the common difference , so we can find out the missing terms now ;

${: \implies \quad \sf T_{2}= T_{1}+(2-1)d}$

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Now

${: \implies \quad \sf T_{3}= T_{1}+(3-1)d}$

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${: \implies \quad \sf T_{3}= 8-6}$

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Also ,

${: \implies \quad \sf T_{4}= T_{1}+(4-1)d}$

${: \implies \quad \sf T_{4}= 8 +3d}$

${: \implies \quad \sf T_{4}= 8-9}$

${: \implies \quad \bf \therefore \: T_{4}= -1}$

Now , The given table can be written as ;

${\begin{array}{|c|c|c|c|c|c|}\cline{1-6} \bf n & \sf 1 & 2 & 3 & 4 & 5 \\ \cline{1-6} \bf T_{n} & \sf 8 & 5 & 2 & -1 & -4 \end{array}}$

Note :- Kindly view the answer from web , if you're not able to see the full answer from here ;

brainly.com/question/26750175

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2 years ago

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Answer:

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Step-by-step explanation:

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Plugging these values into our equation, we get

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