Question

I need some statistics help!!

For a distribution with a standard deviation of σ= 12, describe the location of each of the
following z-scores in terms of its position relative to the mean. For example, = +1.00 is a location that is 12 points above the mean.

a. z = +2.00
Answer:

b. z = +.50
Answer:

c. z= -1.00
Answer:

d. Z= -0.25
Answer:

Answer 1

a. z = +2.00

Answer: The position is 24 points above the mean

b. z = +.50

Answer: The position is 6 points above the mean

c. z= -1.00

Answer: The position is 12 points below the mean

d. Z= -0.25

Answer: The position is 3 points below the mean

Explanation:

We can use the relation,

`z = (x-u)/S`

Where u is the mean and S is the standard deviation,

S = 12,

Rearranging, we get,

`Sz = x - u\\12z=x-u\\12z + u = x`

Where x gives the position relaive to the mean.

So, for z = +1,

we get,

x = u + 12

Hence x is 12 points above the mean (u)

Now answering the questions,

a. z = +2

x = u + (12)(2)

x = u + 24

Hence the position is 24 points above the mean

b. z = +0.50

x = u + 12(o.5)

x = u + 6

hence the position is 6 points above the mean

c. z = -1.00

x = u + 12(-1)

x = u - 12

Hence the position is 12 points below the mean

d. z = -0.25

x = u + (12)(-0.25)

x = u - 3

Hence the position is 3 points below the mean