Statistics Examples

$μ = 4$ , $σ = 1.94$ , $3.65 < x < 4.29$

Step 1

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

$\frac{x - μ}{σ}$

Step 2

Find the z-score.

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Step 2.1

Fill in the known values.

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

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 $- 1$ by $4$ .

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

Step 2.2.1.2

Subtract $4$ from $3.65$ .

$\frac{- 0.35}{1.94}$

Step 2.2.2

Divide $- 0.35$ by $1.94$ .

$- 0.18041237$

Step 3

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

$\frac{x - μ}{σ}$

Step 4

Find the z-score.

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Step 4.1

Fill in the known values.

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

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 $- 1$ by $4$ .

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

Step 4.2.1.2

Subtract $4$ from $4.29$ .

$\frac{0.29}{1.94}$

Step 4.2.2

Divide $0.29$ by $1.94$ .

$0.14948453$

Step 5

Find the value in a look up table of the probability of a z-score of less than $0.07162029$ .

$z = - 0.18041237$ has an area under the curve $0.07162029$

Step 6

Find the value in a look up table of the probability of a z-score of less than $0.05942066$ .

$z = 0.14948453$ has an area under the curve $0.05942066$

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.

$0.05942066 - (- 0.07162029)$

Step 8

Find the area between the two z-scores.

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Step 8.1

Multiply $- 1$ by $- 0.07162029$ .

$0.05942066 + 0.07162029$

Step 8.2

Add $0.05942066$ and $0.07162029$ .

$0.13104096$