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3 years ago

Find the average for each group. Round to nearest tenth. 6.8, 5.6, 3.4, 2.5, and 4.7.

Mathematics

1 answer:

mash [69]3 years ago

3 0

Answer:

4.6

Step-by-step explanation:

Hello!

To find the average we add all the numbers together and divide by how many numbers we added

6.8 + 5.6 + 3.4 + 2.5 + 4.7 = 23

We added 5 numbers so divide the total by 5

23/5 = 4.6

The answer is 4.6

Hope this helps!

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What is the volume of a cube with an edge length of 2.7 centimeters?

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Explanation A random sample of 100 observations from a normally distributed population possesses a mean equal to 83.2 and a stan

Olenka [21]

Answer:

The 95% confidence interval would be given by (81.933;84.467)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=83.2$ represent the sample mean

$\mu$ population mean (variable of interest)

s=6.4 represent the sample standard deviation

n=100 represent the sample size

Confidence interval

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=100-1=99$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,99)".And we see that $t_{\alpha/2}=1.98$

Now we have everything in order to replace into formula (1):

$83.2-1.98\frac{6.4}{\sqrt{100}}=81.933$

$83.2+1.98\frac{6.4}{\sqrt{100}}=84.467$

So on this case the 95% confidence interval would be given by (81.933;84.467)

7 0

3 years ago

4- A manufacturing process produces items whose weights are normally distributed. It is known that 22.57% of all the items produ

galben [10]

Answer:

$\\ \mu = 118\;grams\;and\;\sigma=30\;grams$

Step-by-step explanation:

We need to use z-scores and a standard normal table to find the values that corresponds to the probabilities given, and then to solve a system of equations to find $\\ \mu\;and\;\sigma$ .

<h3>First Case: items from 100 grams to the mean</h3>

For finding probabilities that corresponds to z-scores, we are going to use here a <u>Standard Normal Table </u><u><em>for cumulative probabilities from the mean </em></u><em>(Standard normal table. Cumulative from the mean (0 to Z), 2020, in Wikipedia) </em>that is, the "probability that a statistic is between 0 (the mean) and Z".

A value of a z-score for the probability P(100<x<mean) = 22.57% = 0.2257 corresponds to a value of z-score = 0.6, that is, the value is 0.6 standard deviations from the mean. Since this value is <em>below the mean</em> ("the items produced weigh between 100 grams up to the mean"), then the z-score is negative.

Then

$\\ z = -0.6\;and\;z = \frac{x-\mu}{\sigma}$

$\\ -0.6 = \frac{100-\mu}{\sigma}$ (1)

<h3>Second Case: items from the mean up to 190 grams</h3>

We can apply the same procedure as before. A value of a z-score for the probability P(mean<x<190) = 49.18% = 0.4918 corresponds to a value of z-score = 2.4, which is positive since it is after the mean.

Then

$\\ z =2.4\;and\; z = \frac{x-\mu}{\sigma}$