# 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 denominator.
Rewrite as .
Multiply by .
Simplify.
Combine.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Combine using the product rule for radicals.
Multiply by .
Simplify the numerator.
Multiply by .
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.
Multiply by .
Combine the numerators over the common denominator.
Rewrite in a factored form.
Factor out of .
Reorder the expression.
Reorder and .
Move .
Reorder and .
Factor out of .
Factor out of .
Factor out of .
Apply the distributive property.
Combine and .
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.
Multiply by .
Combine the numerators over the common denominator.
Multiply the numerator by the reciprocal of the denominator.
Combine and .
Move the negative in front of the fraction.
Multiply by .
Simplify.
Combine.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Reduce the expression by cancelling the common factors.
Cancel the common factor.
Rewrite the expression.
Multiply and .
Move to the left of .
Divide by .
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Simplify.
Combine.
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
Multiply by .
Multiply by .
Factor out of .
Separate fractions.
Evaluate the root.
Divide by .
Divide by .
Multiply by .
Multiply .
Multiply by .
Combine and .
Multiply by .
Move the negative in front of the fraction.
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