Binomial Distribution can be defined as the probability distribution of number of successes in an experiment which is run multiple times. For example a coin is flipped 100 times. Here probability of getting head (p) is 0.5. Sample size (n) is 100.

The **mean of the binomial distribution** is calculated as:

$$ μ_{x} = n*p $$

$$ μ_{x} = 100*0.5 $$

The **standard deviation of the binomial distribution** is calculated as:

$$ σ_{x} = \sqrt{n*p*(1−p)} $$

$$ σ_{x} = \sqrt{100*0.5*(1−0.5)} $$

Enter values of sample size and population proportion of success in the calculator below for calculating mean and standard deviation for binomial distribution.

Solution

Step by Step Calculation

$$ μ_{x} = n*p $$

$$ σ_{x} = \sqrt{n*p*(1−p)} $$

Sample size (n) can't be less than or equal to 0. It must be a whole number. Population proportion (p) must lie between 0 and 1.

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