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Liula [17]
4 years ago
11

Determine the difference between the mean and standard deviation of: 33, 44, 43, 56, 55, and 30.​

Mathematics
1 answer:
lorasvet [3.4K]4 years ago
4 0

Answer:

mean = ( 33+44+43+56+55+30) / 6

= 261/6

= 43.5

variance =  \frac{33 { }^{2} +  {44}^{2}  +  {43}^{2}  +  {56}^{2} +  {55}^{2}  +  {30}^{2}   }{6}  -  {43.5}^{2}

variance = 96.92

standard deviation = √96.92

= 9.84

difference between mean and standard deviation

= 43.5 - 9.84

= 33.66

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Answer below

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ziro4ka [17]

Answer:

a) \frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}

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Now we just take square root on both sides of the interval and we got:

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Step-by-step explanation:

423.6, 487.3, 453.2, 402.9, 483.0, 477.7, 442.3, 418.4, 459.0

Part a

The confidence interval for the population variance is given by the following formula:

\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}

On this case we need to find the sample standard deviation with the following formula:

s=sqrt{\frac{\sum_{i=1}^8 (x_i -\bar x)^2}{n-1}}&#10;And in order to find the sample mean we just need to use this formula:&#10;[tex]\bar x =\frac{\sum_{i=1}^n x_i}{n}

The sample deviation for this case is s=30.23

The next step would be calculate the critical values. First we need to calculate the degrees of freedom given by:

df=n-1=9-1=8

The Confidence interval is 0.98 or 98%, the value of \alpha=0.02 and \alpha/2 =0.01, and the critical values are:

\chi^2_{\alpha/2}=20.09

\chi^2_{1- \alpha/2}=1.65

And replacing into the formula for the interval we got:

\frac{(8)(30.23)^2}{20.09} \leq \sigma^2 \leq \frac{(8)(30.23)^2}{1.65}

363.90 \leq \sigma^2 \leq 4430.80

Now we just take square root on both sides of the interval and we got:

19.08 \leq \sigma \leq 66.56

Part b

For this case we are 98% confidence that the true deviation for the population of interest is between 19.08 and 66.56

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Answer:

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Step-by-step explanation:

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