# Statistics Examples

Use the Table to Find the z-Score
, ,
Find the mean of the binomial distribution using the formula.
Find the population proportion.
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 expression.
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.

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