14 terms

# CH 10: The normal distribution

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the normal distribution
a continuous probability distribution describing a bell-shaped curve. It is a good approximation to the frequency distribution of many biological variables
formula for the normal distribution
includes two main parameters:
u = mean of the distribution
o= standard deviation
Properties of the normal distribution
1. continuous distribution, probability is measured by the area under the curve (not the height)
2. it is symmetric around its mean
3. it has a single mode
4. the probability density is highest exactly at the mean
5. the mean, mode, and median are al equal
rule of thumbs for normal distributions
two thirds of the area lie within one standard deviation of the mean:
u ± o
95% of the probability of a normal distribution lies with in 1.96 standard deviations of the mean:
u ± 1.96o
the standard normal distribution
the standard normal distribution is a normal distribution with mean of 0 and SD of 1; Z = a variable having a standard normal distribution
a.bc table
abc refer to the digits of the number; the pr that Z is greater than a.bc is given in the table
table doesnt give pr for negative numbers however...
symmetric distribution around the mean states:
pr[Z < - number] = pr [Z > numbe]
pr of Z between a lower and upper bound
Pr[lower bound< Z < upper bound] = Pr [Z > lower bound] - Pr [ > upper bound]
standard normal distribution to describe any normal distribution
Z = (Y - u)/o
Z = standard normal deviate
converts Y, which has a normal distribution with mean u and SD o, which has a standard normal distribution;
how far Y is from its mean measured by number of standard deviations
Standard normal deviate
Z; tells us how many standard deviations a particular value is from the mean
normal distribution of sample means
If a variable Y has a normal distribution in a population, then the distribution of sample means Y is also normal; always equals the mean of the original distribution (u) but with a smaller standard deviation aka the standard deviation of the mean
standard deviation of the mean (standard error)
o(y) = o/√n
central limit theorem (1)
the sum or mean of a large number of measurements randomly sampled from a non-normal population is approximately normally distributed
central limit theorem (2)
when the number of trials n is large, the binomial probability distribution for the number of successes is approximated by a normal distribution having mean np and standard deviation √np(1-p)