10. The Normal Distribution Flashcards
What two values are required to calculate normal distribution?
mean and variance
What can a normal distribution be fully described by?
it’s mean and standard deviation
characteristics of a normal distribution
single mode
bell curve shape
symmetric around it’s mean
center of distribution is at mean
mean, median, and mode are ALL THE SAME
mean
mathematical average
relationship between standard deviation and variance
variance = (standard deviation)^2
median
the middle number if values are listed in order
mode
most frequently occurring number in a set of numbers
about 2/3 of random draws from a normal distribution are…
within one standard deviation of the mean
random draws = all possible values
2 standard deviations from mean captures how much of possible answers
95%!!!
95% of time when you get a value it will be 2 or less standard deviations from mean
Standard normal distribution
normal distribution where mean is 0 and standard deviation is one
u = 0
sigma = 1
Standard normal table
gives the probability of getting a random draw from a standard normal distribution greater than a given value
relationship between Pr on either tail
Pr[Z > x] = Pr[Z < - x]
total area under a normal distribution = …. THEREFORE
1
Pr[Z < x] = 1 - Pr[Z > x]
In standard normal distribution, what is the the probability of something being grater than 1.96
2.5%
trick for finding prob of area between lower bound and upper bound
prob of being greater than lower bound - prob of being greater than upper bound
how to translate any normal distribution to standard normal distribution
Z = (Y - u) / sigma
Z = standard normal deviate, scale between sd 0 and 1
Y = variable we care about
u = mean of distribution
sigma = standard deviation
- how different is this value from the mean in units of standard deviation/how for from mean is Y in units of standard deviation
Application of Z
can convert any value from normal distribution to Z, which would be corresponding value in standard normal distribution.
Probability of getting a value greater than Y is the same as the probability of getting a value greater than Z from a standard normal distribution
properties of Z ARE the properties of Y
If the variable we care about has a normal distribution, the sample means…
are also normally distributed
The mean of the sample (symbol)
u
Standard deviation of a sample mean formula (standard error)
sigma Y bar = sigma / sqrt(n)
Standard error def
standard error of an estimate of a mean is the standard deviation of the distribution of sample means
Standard error can be approximated by
NOT TALKED ASBT YET
difference between normal distribution for a variable and the mean
same mean, but different standard deviation
smaller deviation for means!!!
larger samples equals ____ standard errors
smaller, because divided by sqrt(n)
