Statistics Examples

$n = 119$ , $p = 0.42$ , $x = 65$

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.

$(119) (0.42)$

Step 1.3

Multiply $119$ by $0.42$ .

$49.98$

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.

$\sqrt{(119) (0.42) (0.58000004)}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Multiply $119$ by $0.42$ .

$\sqrt{49.98 \cdot 0.58000004}$

Step 2.3.2

Multiply $49.98$ by $0.58000004$ .

$\sqrt{28.988401\overline{9}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{28.988401\overline{9}}$

Decimal Form:

$5.38408785 \dots$

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