Statistics Examples

Approximate Using the Normal Distribution
, ,
Find the mean of the binomial distribution.
The mean of the binomial distribution can be found using the formula.
Fill in the known values.
Multiply by to get .
Find the standard deviation of the binomial distribution.
The standard deviation of the binomial distribution can be found using the formula.
Fill in the known values.
Simplify the expression.
Multiply by to get .
Multiply by to get .
Multiply by to get .
Evaluate the root.
Use the calculated values to find the z-score.
The z-score for a value of a random variable is the number of standard deviations that falls from the mean .
The z-score converts a non-standard distribution to a standard distribution in order to find the probability of an event.
Find the z-score.
Fill in the known values.
Simplify the expression.
Simplify the numerator.
Multiply by to get .
Subtract from to get .
Divide by to get .