The normal distribution Flashcards
characteristics
- probabilities that are a range of values
- probabilities are the areas under the curve
- total area under a probability density curve = 1
density curves
area = relative frequency and adds to 1
for comparison, curves are often scaled to have a total area of 1
might be a histogram
features of the density curve
on or above the horizontal axis
area of 1 underneath
the area under the curve between any two values is the proportion of all observations that lie in that range
not all bell-shaped
mode
a density, the location where the curve is highest; represents the region in which the random variable is most likely
median
the point with half the total area on each side that is, with half the population below the value and a half above
mean
the average value of the population
normal distributions are histograms of
heights of women, IQ of an age cohort etc.
- tend to look similar
- scaled so the area under curve is 1
- density curves are symmetric, unimodal, bell-shaped
- median = mode = mean due to symmetry
the 68-95-99.7 rule
normal distribution with mean mew and SD
- 68% of observations lie in one SD or mean
- 95% within two of mew
- 99.7% lie in three
notation of normals
N(mew, SD) if X is the value of a person selected at random, X~N(mew, SD)
there is a probability function equation as well
standardising observations
if x is an observation from a population that has mew and SD, the standardised value of x is
Z = x-mew/SD
this is a Z score which tells us how many sample SD the original observation falls away from the sample mean and in which direction
this equation produces a new variable with mean 0 and SD 1 and helps with comparisons
working out area under a curve
once variables are standardised, the probabilities are the same
can use 68-95-99.7 rule to work this out
or use NORMDIST in excel
