Statistics Examples

$μ = 4$ , $σ = 1.94$ , $3.61 < x < 4.26$

Step 1

The z-score converts a non-standard distribution to a standard distribution in order to find the probability of an event.

$\frac{x - μ}{σ}$

Step 2

Find the z-score.

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Step 2.1

Fill in the known values.

$\frac{3.61 - (4)}{1.94}$

Step 2.2

Simplify the expression.

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Step 2.2.1

Simplify the numerator.

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Step 2.2.1.1

Multiply $- 1$ by $4$ .

$\frac{3.61 - 4}{1.94}$

Step 2.2.1.2

Subtract $4$ from $3.61$ .

$\frac{- 0.39}{1.94}$

Step 2.2.2

Divide $- 0.39$ by $1.94$ .

$- 0.20103092$

Step 3

The z-score converts a non-standard distribution to a standard distribution in order to find the probability of an event.

$\frac{x - μ}{σ}$

Step 4

Find the z-score.

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Step 4.1

Fill in the known values.

$\frac{4.26 - (4)}{1.94}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Simplify the numerator.

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Step 4.2.1.1

Multiply $- 1$ by $4$ .

$\frac{4.26 - 4}{1.94}$

Step 4.2.1.2

Subtract $4$ from $4.26$ .

$\frac{0.26}{1.94}$

Step 4.2.2

Divide $0.26$ by $1.94$ .

$0.13402061$

Step 5

Find the value in a look up table of the probability of a z-score of less than $0.0796902$ .

$z = - 0.20103092$ has an area under the curve $0.0796902$

Step 6

Find the value in a look up table of the probability of a z-score of less than $0.05333842$ .

$z = 0.13402061$ has an area under the curve $0.05333842$

Step 7

To find the area between the two z-scores, subtract the smaller z-score value from the larger one. For any negative z-score, change the sign of the result to negative.

$0.05333842 - (- 0.0796902)$

Step 8

Find the area between the two z-scores.

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Step 8.1

Multiply $- 1$ by $- 0.0796902$ .

$0.05333842 + 0.0796902$

Step 8.2

Add $0.05333842$ and $0.0796902$ .

$0.13302863$