Mathematics, 11.06.2020 17:57 eddie6242

Is a measure of 22 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 22 inches from 16 inches? (b) Is 22 inches far away from a mean of 16 inches? (c) Suppose the standard deviation of the underlying data is 4 inches. Is 22 inches far away from a mean of 16 inches?

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Answer from: Kana81

a) 3 standard deviations above 16

b) More than 2 standard deviations of the mean, so yes, 22 inches is faw away from the mean of 16 inches.

c) Less than 2 standard deviations, so not far away.

Step-by-step explanation:

Z-score:

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore 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. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

If Z < -2 or Z > 2, X is considered to be far away from the mean.

In this question, we have that:

$\mu = 16$

(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 22 inches from 16 inches?

This is Z when $X = 22, \sigma = 2$ .

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

$Z = \frac{22 - 16}{2}$

Z = 3

So 22 inches is 3 standard deviations fro 16 inches.

(b) Is 22 inches far away from a mean of 16 inches?

3 standard deviations, more than two, so yes, 22 inches is far away from a mean of 16 inches.

Now $\sigma = 4$

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

$Z = \frac{22 - 16}{4}$

Z = 1.5

1.5 standard deviations from the mean, so 22 inches is not far away from the mean.

Answer from: Quest

(d)

step-by-step explanation:

given: the line in the graph passes through points (5,30) and (6,26).

then, the equation of line is:

$y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})$

$y-30=\frac{26-30}{6-5}(x-5)$

$y-30=-4(x-5)$

$y-30=-4x+20$

$y=-4x+50$

now, put y=a(n) and x=n,

$a(n)=-4n+50$

$a(n)=-4n+46+4$

$a(n)=46-(n-1){\times}4$

hence, option d is correct.

Ascientist cools some water at a constant rate. the graph and table show how the temperature of the

Answer from: Quest

the correct answer is b. negative exponential growth.

step-by-step explanation:

you can tell it's an exponential function because it decreases rapidly then levels out and never touches the x-axis.

it is negative because the y-axis decreases as the x-axis increases.

therefore it is a negative exponential growth graph.

hope i !

Categorize the graph as linear increasing, linear decreasing, exponential growth, or negative expone

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