Finite Math Examples

$n = 2$ ,

$x = 22$ ,

$σ = 10$ ,

$α = 0.95$

Step 1

Find the mean of the binomial distribution.

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Step 1.1

The mean of the binomial distribution can be found using the formula.

$μ = n p$

Step 1.2

Fill in the known values.

$2$

Step 1.3

Remove parentheses.

$2$

Step 2

Find the standard deviation of the binomial distribution.

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Step 2.1

The standard deviation of the binomial distribution can be found using the formula.

$σ = \sqrt{n p q}$

Step 2.2

Fill in the known values.

$\sqrt{2}$

Step 2.3

Remove parentheses.

$\sqrt{2}$

Step 3

Use the calculated values to find the z-score.

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Step 3.1

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 3.2

Find the z-score.

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Step 3.2.1

Fill in the known values.

$\frac{22 - (2)}{10}$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Cancel the common factor of

$22 - (2)$ and

$10$ .

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Step 3.2.2.1.1

Rewrite

$22$ as

$- 1 (- 22)$ .

$\frac{- 1 (- 22) - (2)}{10}$

Step 3.2.2.1.2

Factor

$- 1$ out of

$- 1 (- 22) - (2)$ .

$\frac{- 1 (- 22 + 2)}{10}$

Step 3.2.2.1.3

Factor

$2$ out of

$- 1 (- 22 + 2)$ .

$\frac{2 (- 1 (- 11 + 1))}{10}$

Step 3.2.2.1.4

Cancel the common factors.

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Step 3.2.2.1.4.1

Factor

$2$ out of

$10$ .

$\frac{2 (- 1 (- 11 + 1))}{2 (5)}$

Step 3.2.2.1.4.2

Cancel the common factor.

$\frac{2 (- 1 (- 11 + 1))}{2 \cdot 5}$

Step 3.2.2.1.4.3

Rewrite the expression.

$\frac{- 1 (- 11 + 1)}{5}$

Step 3.2.2.2

Simplify the expression.

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Step 3.2.2.2.1

Add

$- 11$ and

$1$ .

$\frac{- 1 \cdot - 10}{5}$

Step 3.2.2.2.2

Multiply

$- 1$ by

$- 10$ .

$\frac{10}{5}$

Step 3.2.2.2.3

Divide

$10$ by

$5$ .

$2$