Finite Math Examples

n = 40

$n = 40$ ,

p = 0.69

$p = 0.69$ ,

x = 38

$x = 38$

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

$μ = n p$

Step 1.2

Fill in the known values.

(40) (0.69)

$(40) (0.69)$

Step 1.3

Multiply

40

$40$ by

0.69

$0.69$ .

27.6

$27.6$

27.6

$27.6$

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}

$σ = \sqrt{n p q}$

Step 2.2

Fill in the known values.

\sqrt{(40) (0.69) (0.31)}

$\sqrt{(40) (0.69) (0.31)}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Multiply

40

$40$ by

0.69

$0.69$ .

\sqrt{27.6 \cdot 0.31}

$\sqrt{27.6 \cdot 0.31}$

Step 2.3.2

Multiply

27.6

$27.6$ by

0.31

$0.31$ .

\sqrt{8.556}

$\sqrt{8.556}$

\sqrt{8.556}

$\sqrt{8.556}$

\sqrt{8.556}

$\sqrt{8.556}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\sqrt{8.556}

$\sqrt{8.556}$

Decimal Form:

2.92506410 \dots

$2.92506410 \dots$

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