Math  /  Data & Statistics

Questionthis distribution that corresponds to the given z -score. z=7z=-7
The data item that corresponds to z=7\mathrm{z}=-7 is \square . (Type an integer or a decimal.)

Studdy Solution

STEP 1

1. The distribution is normal with a mean (μ\mu) of 100.
2. The standard deviation (σ\sigma) is 60.
3. The z-score formula is z=Xμσ z = \frac{X - \mu}{\sigma} , where X X is the data item.

STEP 2

1. Set up the z-score equation.
2. Solve for the data item X X .

STEP 3

Set up the z-score equation using the given values:
z=Xμσ z = \frac{X - \mu}{\sigma}
Substitute z=7 z = -7 , μ=100 \mu = 100 , and σ=60 \sigma = 60 :
7=X10060 -7 = \frac{X - 100}{60}

STEP 4

Solve for X X :
Multiply both sides by 60 to isolate X100 X - 100 :
7×60=X100 -7 \times 60 = X - 100
420=X100 -420 = X - 100
Add 100 to both sides to solve for X X :
X=420+100 X = -420 + 100
X=320 X = -320
The data item that corresponds to z=7 z = -7 is:
320 \boxed{-320}

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