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3 years ago

If a data value in a normal distribution has a negative z-score, which of the following must be true?

Mathematics

2 answers:

Fynjy0 [20]3 years ago

8 0

Answer:

C. The data value must be less than the mean.

Step-by-step explanation:

We have been given a statement and we are asked to choose the correct option about our given statement.

Since a z-score tells us that a data value is how many standard deviation away from mean.

To find the z-score for a given data value or raw score, we subtract the mean of data set from the given raw score and divide the result by standard deviation of the data set

If a data value is greater than mean, then it will have a positive z-score. If a data value is smaller than mean, then it will have a negative z-score.

Upon looking at our given choices we can see that option C is the correct choice.

Tamiku [17]3 years ago

4 0

<span>The data value must be less than the mean.</span>

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Answer:

Each landing is about 17 inches.

The vertical rise from Floor 1 to Floor 2 is about 7 feet.

Step-by-step explanation:

Please refer to the attachment below. (I accidentally wrote 30.30 instead of 30.20. Please ignore that and sorry for any confusion.)

Part A)

So, we want to find the length of $\ell$ .

Note that the angle of elevation, the vertical height, and $\ell$ form a right triangle.

Since the vertical height opposite to our angle is 10, and we want to find the adjacent height, we can use the tangent ratio:

$\displaystyle \tan(x^\circ)=\frac{\text{Opposite}}{\text{Adjacent}}$

Therefore:

$\displaystyle \tan(30.20)=\frac{10}{\ell}$

Solve for $\ell$ . Cross-multiply:

$\displaystyle \ell\tan(30.20)=10$

So:

$\displaystyle \ell=\frac{10}{\tan(30.20)}=17.1817...\approx17\text{ inches}$

The landing space per step is about 17 inches.

Part B)

We know that there are a total of 12 feet of horizontal space total for each landing.

12 feet is equivalent to (12)(12) = 144 inches.

Since each landing is 17.1817... inches, this means that we have 144/(17.1817...) = 8.38... or about 8 steps.

Since the vertical rise of each step is 10 inches, the vertical rise from the 1st Floor to the second will be 8(10) or 80 inches or 80/12 = 6.666... or about 7 feet.

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