Statistics Examples

$n = 52$ ,

$p = 0.45$ ,

$x = 37$

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.

$(52) (0.45)$

Step 1.3

Multiply

$52$ by

$0.45$ .

$23.4$

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.

$\sqrt{(52) (0.45) (0.55)}$

Step 2.3

Simplify the expression.

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Step 2.3.1

Multiply

$52$ by

$0.45$ .

$\sqrt{23.4 \cdot 0.55}$

Step 2.3.2

Multiply

$23.4$ by

$0.55$ .

$\sqrt{12.87}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{12.87}$

Decimal Form:

$3.58747822 \dots$

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