Finite Math Examples Statistical Distributions

Approximate Using the Normal Distribution

$n = 50$ , $p = 0.4$ , $x = 28$

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.

$(50) (0.4)$

Step 1.3

Multiply $50$ by $0.4$ .

$20$

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.

$\sqrt{(50) (0.4) (0.6)}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Multiply $50$ by $0.4$ .

$\sqrt{20 \cdot 0.6}$

Step 2.3.2

Multiply $20$ by $0.6$ .

$\sqrt{12}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{12}$

Decimal Form:

$3.46410161 \dots$

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Approximate Using the Normal Distribution

Statistical Distributions

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