Mathematics, 05.10.2019 03:20 blacee01

Is a measure of 26 inches "far away" from a mean of 16 inches? as someone with knowledge of statistics, you answer "it depends" and request the standard deviation of the underlying data. (a) suppose the data come from a sample whose standard deviation is 2 inches. how many standard deviations is 26 inches from 16 inches? (b) is 26 inches far away from a mean of 16 inches? (c) suppose the standard deviation of the underlying data is 7 inches. is 26 inches far away from a mean of 16 inches?

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Answer from: jesh0975556

Using z-scores, it is found that:

a) 26 inches is 5 standard deviations from 16 inches.b) |Z| = 5 > 2, thus yes, 26 inches is far away from a mean of 16 inches.c) |Z| = 1.43 < 2, thus, 26 inches is not far away from a mean of 16 inches.

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In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. If |Z| > 2, the measure is said to be far from the mean.

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Mean of 16 means that $\mu = 16$ .Measure of 26 means that X = 26

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Item a:

Standard deviation of 2, thus $\sigma = 2$ .

The z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{26 - 16}{2}$

Z = 5

Thus, 26 inches is 5 standard deviations from 16 inches.

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Item b:

|Z| = 5 > 2, thus yes, 26 inches is far away from a mean of 16 inches.

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Item c:

Standard deviation of 7, thus, $\sigma = 7$

The z-score is:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{26 - 16}{7}$

Z = 1.43

|Z| = 1.43 < 2, thus, 26 inches is not far away from a mean of 16 inches.

A similar problem is given at link

Answer from: mrstealyogirl40

Hello!

In a normal distribution, between the mean and the mean plus the standar deviation, there is a 34.1% of the data set, between the mean plus the standar deviation, and the mean between two times the standard deviation, there is a 16.2% of the data set, and so on.

If our mean is 16 inches, and the measure is 26 inches, then the difference is 10 inches between them.

a) if the standar deviation is 2 inches, then you are 10/2 = 5 standar deviations from the mean.

b) yes, is really far away from the mean, in a normal distribution a displacement of 5 standar deviations has a very small probability.

c) Now the standar deviation is 7, so now 26 is in the range between 1 standar deviation and 2 standar deviations away from the mean.

Then this you have a 16% of the data, then in this case, 26 inches is not far away from the mean.

Answer from: Quest

answer: answer

step-by-step explanation:

Answer from: Quest

38+105= 143, 39+104=143, and you will find then adding the numbers on opposite sides, moving inwards yields the answer 138 every time. because of this, you’re going to multiply 138 times the number of pairs, which is 34. therefore, 34*138= 4692(i’m sorry if it’s the wrong numbers, but it’s the right concept)
I’m not sure how to solve these type of problems

I’m not sure how to solve these type of problems

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Is a measure of 26 inches "far away" from a mean of 16 inches? as someone with knowledge of statist...

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