# Statistics Examples

, ,

Find the mean of the binomial distribution using the formula.

The population proportion is the number of true results divided by the total samples .

Fill in the known values.

Simplify the expression.

Fill in the known values to find .

Simplify the numerator.

Multiply by to get .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine the numerators over the common denominator.

Apply the distributive property.

Rewrite as .

Multiply by .

Simplify.

Simplify .

Move the negative in front of the fraction.

Multiply by to get .

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine the numerators over the common denominator.

To write as a fraction with a common denominator, multiply by .

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine the numerators over the common denominator.

Multiply by to get .

Remove parentheses.

Multiply the numerator by the reciprocal of the denominator.

Simplify the denominator.

Multiply the numerator by the reciprocal of the denominator.

Multiply by to get .

Cancel the common factor of .

Simplify.

Factor out of .

Reduce the expression by cancelling the common factors.

Simplify the denominator.

-----Begin simplification-----

Multiply by to get .

Divide by to get .

Evaluate the root.

Multiply the numerator by the reciprocal of the denominator.

Divide by to get .

Simplify .

Write as a fraction with denominator .

Multiply and to get .

Simplify the expression.

Move to the left of the expression .

Multiply by to get .

Move .

Move .

Factor out of .

Factor out of .

Rewrite as .

Move .

Multiply by to get .

Factor out of .

Simplify the expression.

Rewrite as .

Move the negative in front of the fraction.