Statistics Examples

μ = 4

$μ = 4$ ,

σ = 1.94

$σ = 1.94$ ,

3.65 < x < 4.29

$3.65 < x < 4.29$

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}

$\frac{x - μ}{σ}$

Step 2

Find the z-score.

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Step 2.1

Fill in the known values.

\frac{3.65 - (4)}{1.94}

$\frac{3.65 - (4)}{1.94}$

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

$- 1$ by

4

$4$ .

\frac{3.65 - 4}{1.94}

$\frac{3.65 - 4}{1.94}$

Step 2.2.1.2

Subtract

4

$4$ from

3.65

$3.65$ .

\frac{- 0.35}{1.94}

$\frac{- 0.35}{1.94}$

\frac{- 0.35}{1.94}

$\frac{- 0.35}{1.94}$

Step 2.2.2

Divide

- 0.35

$- 0.35$ by

1.94

$1.94$ .

- 0.18041237

$- 0.18041237$

- 0.18041237

$- 0.18041237$

- 0.18041237

$- 0.18041237$

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}

$\frac{x - μ}{σ}$

Step 4

Find the z-score.

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Step 4.1

Fill in the known values.

\frac{4.29 - (4)}{1.94}

$\frac{4.29 - (4)}{1.94}$

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

$- 1$ by

4

$4$ .

\frac{4.29 - 4}{1.94}

$\frac{4.29 - 4}{1.94}$

Step 4.2.1.2

Subtract

4

$4$ from

4.29

$4.29$ .

\frac{0.29}{1.94}

$\frac{0.29}{1.94}$

\frac{0.29}{1.94}

$\frac{0.29}{1.94}$

Step 4.2.2

Divide

0.29

$0.29$ by

1.94

$1.94$ .

0.14948453

$0.14948453$

0.14948453

$0.14948453$

0.14948453

$0.14948453$

Step 5

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

0.07162029

$0.07162029$ .

z = - 0.18041237

$z = - 0.18041237$ has an area under the curve

0.07162029

$0.07162029$

Step 6

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

0.05942066

$0.05942066$ .

z = 0.14948453

$z = 0.14948453$ has an area under the curve

0.05942066

$0.05942066$

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.

0.05942066 - (- 0.07162029)

$0.05942066 - (- 0.07162029)$

Step 8

Find the area between the two z-scores.

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Step 8.1

Multiply

- 1

$- 1$ by

- 0.07162029

$- 0.07162029$ .

0.05942066 + 0.07162029

$0.05942066 + 0.07162029$

Step 8.2

Add

0.05942066

$0.05942066$ and

0.07162029

$0.07162029$ .

0.13104096

$0.13104096$

0.13104096

$0.13104096$