The standard deviation is the square root of the variance. The binomial distribution generates probabilities arising in a repeated experiment with only two possible outcomes for each repeated trial. As the number of trials increases, the distribution of X becomes more symmetric. If np and nq equal at least five, the binomial distribution of X may be approximated by the normal distribution. A continuous distribution is represented by a smooth curve.
Probability is represented by the area under the curve.
The normal distribution is the most common continuous distribution in statistics. Many variables in the social sciences are normally distributed. The normal distribution is a formula that draws a family of symmetric curves. Each distinct normal curve has its own mean and variance. The normal curve extends from negative to positive infinity.