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Consider a value to be significantly low if its z score less than or equal to minus−2 or consider a value to be significantly hi

katrin2010 [14]

Answer:

Test scores of 10.2 or lower are significantly low.

Test scores of 31.4 or higher are significantly high.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

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.

In this problem, we have that:

$\mu = 20.8, \sigma = 5.3$

Identify the test scores that are significantly low or significantly high.

Significantly low

Z = -2 and lower.

So the significantly low scores are thoses values that are lower or equal than X when Z = -2. So

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

$-2 = \frac{X - 20.8}{5.3}$

$X - 20.8 = -2*5.3$

$X = 10.2$

Test scores of 10.2 or lower are significantly low.

Significantly high

Z = 2 and higher.

So the significantly high scores are thoses values that are higherr or equal than X when Z = 2. So

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

$2 = \frac{X - 20.8}{5.3}$

$X - 20.8 = 2*5.3$

$X = 31.4$

Test scores of 31.4 or higher are significantly high.

3 0

3 years ago

If the mean of 4,6,4,7,(x+1),8 and 2 is 5 ,find the median

Rainbow [258]

<h3>Answer: Median = 4</h3>

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Explanation:

The mean is found by adding up all of the values and dividing by n, where n is the number of values in the set.

In this case, we have n = 7 values here. We count (x+1) as well since x is a placeholder for a number, which makes (x+1) also a placeholder in a sense.

As for what replaces x, we're not sure yet but we can use algebra to solve.

Lets add up all of the values given except for the "5" at the end. That 5 is the mean which is not part of the data set.

Adding up those values mentioned gives:

4+6+4+7+(x+1)+8+2 = x+32

Then divide this over n = 7 to get the mean 5

(x+32)/n = mean

(x+32)/7 = 5

-----------------------------

Let's isolate x

(x+32)/7 = 5

x+32 = 7*5

x+32 = 35

x = 35-32

x = 3

If x = 3, then x+1 = 3+1 = 4

So the (x+1) is being a placeholder for the number 4.

In other words, we'll replace the (x+1) with 4.

The data set of

4,6,4,7,(x+1),8,2

updates to

4,6,4,7,4,8,2

-----------------------------

We'll get to the median in a moment, but first we need to check if we have the correct replacement for (x+1)

Add up the values in the set {4,6,4,7,4,8,2}

Doing so leads to: 4+6+4+7+4+8+2 = 35

Then divide by n = 7 to compute the mean: 35/n = 35/7 = 5

We get the mean is 5 which matches with the instructions. So we have the correct replacement for the (x+1). We can now find the median.

------------------------------

To find the median of any data set, we need to make sure the numbers are in order from smallest to largest.

Right now {4,6,4,7,4,8,2} is not sorted, but we can sort the items to get {2,4,4,4,6,7,8}

The median is at the exact middle. In this set, the median is that third copy of '4'. Note how "2,4,4" is to the left of the median while "6,7,8" is to the right of the median. There is the same number of values on either side of the median to show things are balanced and we are at the center point.

As an alternative, you can cross off each pair of outer values one at a time until you steadily arrive at the midpoint, which again is that third copy of '4'.

So that's why the median is 4.

8 0

3 years ago

What is the value of -2(x + 3)

matrenka [14]

Answer:

2x+6 period

5 0

3 years ago

Solve and graph the inequality 16x<-64

WITCHER [35]

Answer:

75 po ang sagot