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When studying the sum (or average) of a large number of independent variables.
A large number is necessary for the Central Limit Theorem to kick in - unless the variables themselves were normally distributed.
Independence is critical. If they are not, normality may not be assumed.
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For the normal distribution does it always require a continuity correction?
Use the continuity correction when using the normal distribution to approximate a binomial distribution to take into account the binomial is a discrete distribution and the normal distribution is continuous.
How does the standard normal distribution differ from the t-distribution?
The normal distribution and the t-distribution are both symmetric bell-shaped continuous probability distribution functions. The t-distribution has heavier tails: the probability of observations further from the mean is greater than for the normal distribution. There are other differences in terms of when it is appropriate to use them. Finally, the standard normal distribution is a special case of a normal distribution such that the mean is 0 and the standard deviation is 1.
When we use f distribution?
When comparing the sums of squares of normal variates.
Does a normal probability distribution include a bimodal distribution?
No, the normal distribution is strictly unimodal.
Is normal distribution also a probability distribution?
Yes. When we refer to the normal distribution, we are referring to a probability distribution. When we specify the equation of a continuous distribution, such as the normal distribution, we refer to the equation as a probability density function.
