Contents
Why is normal distribution not a good model?
There is a probability of about 3.4% that a normally distributed random variable is more than 1.836 standard deviation units above the mean. So at the upper end of the range at least, the normal with the given mean and standard deviation gives a poor fit.
How does T distribution differ from a normal distribution?
The T distribution is similar to the normal distribution, just with fatter tails. Both assume a normally distributed population. T distributions have higher kurtosis than normal distributions. The probability of getting values very far from the mean is larger with a T distribution than a normal distribution.
Why are some distributions not normal?
Insufficient Data can cause a normal distribution to look completely scattered. An extreme example: if you choose three random students and plot the results on a graph, you won’t get a normal distribution. You might get a uniform distribution (i.e. 62 62 63) or you might get a skewed distribution (80 92 99).
How is normal distribution misused?
The commonest misuse here is to assume that somehow the data must approximate to a normal distribution, when in fact non-normality is much more common. The normal distribution underlies much of statistical theory, and many statistical tests require the errors, or the test statistic, represent a normal distribution.
What should the mean and standard deviation of a normal distribution be?
The data follows a normal distribution with a mean score (M) of 1150 and a standard deviation (SD) of 150. Following the empirical rule: Around 68% of scores are between 1000 and 1300, 1 standard deviation above and below the mean. Around 95% of scores are between 850 and 1450, 2 standard deviations above and below the mean.
Why is it important to know the standard score?
The standard score (more commonly referred to as a z-score) is a very useful statistic because it (a) allows us to calculate the probability of a score occurring within our normal distribution and (b) enables us to compare two scores that are from different normal distributions.
Do you need to know the formula for the normal distribution?
The normal distribution is a probability distribution, so the total area under the curve is always 1 or 100%. The formula for the normal probability density function looks fairly complicated. But to use it, you only need to know the population mean and standard deviation.
How is the probability of a score calculated?
Therefore, statisticians have come up with probability distributions, which are ways of calculating the probability of a score occurring for a number of common distributions, such as the normal distribution. In our case, we make the assumption that the students’ scores are normally distributed.