Download Describe, in your own words, the following terms and give an

Describe, in your own words, the following terms and give an example of each.
Probability
Binomial experiment
Population parameter
Probability distribution
Standard score
Central limit theorem
Standard error of the mean
Normal distribution
Standard normal distribution
Continuity correction factor
Term
Probability
Definition
Example
Probability is the chance that a
If we rolled a standard 6-faced fair die
particular outcome will occur when a
once, the probability of getting a 6 is
random experiment (such as tossing a
1/6; that is, if the die is rolled
fair coin) is performed. Probability of
repeatedly n number of times, in the
an event A is the ratio of the number
long run, we can expect 6 to occur
of favorable outcomes to the total
approximately (n/6) times.
number of outcomes.
Binomial Experiment
An experiment that has the
Tossing a fair coin. Here, the
characteristic that the probability of
probability of success (say, Head) in
success remains the same no matter
any toss is the same, that is ½.
how many times the experiment is
repeated.
A parameter is a value (usually
Population Parameter
Average monthly salary of professors
unknown and which therefore has to
be estimated), used to represent a
certain statistic.
Probability Distribution
Probability distribution of a variable
Binomial distribution (Discrete),
(discrete or continuous) is a list of
Normal distribution (Continuous)
probabilities associated with each of
its possible values. It is also called
probability mass function or simply
probability function.
Standard Score
The standard score is the distance
If a population has a mean of 15 and a
that an observation (or statistic) is
standard deviation of 2.5. Then the
from the mean of its distribution in
observation 17.5 would have a
terms of its standard deviation units.
standard score = (17.5 - 15)/2.5 = 1.
Central Limit Theorem
The central limit theorem says that
If samples of size n are drawn from a
the sample means follow an
population, the sample mean(x-bar)
increasingly normal distribution as the
will be close to the population mean
sample size increases. In particular,
() whereas the sample standard
the mean of the sampling distribution
deviation, s = Population standard
is the same as that of the population
deviation,/n
and the standard deviation is the
population standard deviation divided
by the square root of the sample size.
Hence, the larger the sample, the
smaller the standard deviation of the
sampling distribution.
Standard Error of the Mean
The standard error of the mean is the
For a sample of size 16 with a
standard deviation of the sampling
population standard deviation of 5,
distribution. In particular, it is the
the standard error of the mean is
population standard deviation divided
5/16 = 1.25
by the square root of the sample size,
that is s = /n.
Normal Distribution
The normal distribution is a
The diameters of bolts produced by a
continuous, real valued, symmetric,
machine may be normally distributed
bell-shaped distribution with two
with a mean of 0.75 inches and a
parameters, the mean () and the
standard deviation of 0.25 inch.
standard deviation ().
It is a particular type of normal
A normal distribution with  = 0 and
distribution with mean of  = 0 and
 = 1.
standard deviation of  = 1. Problems
on normal distribution are usually
solved by using this distribution.
Because there are an infinite number
Standard Normal Distribution
of possible normal distributions, one
table (the standard normal table) is
used to calculate all normal
probabilities. Finding standard scores
(z- scores) transforms any normal
distribution into a standard normal
distribution.
Continuity Correction Factor
A correction factor that is used when
To find the probability of getting 623
binomial probabilities are calculated
heads when a fair coin is tossed 1000
using the normal distribution
times,
assumption.
n = 1000, p = ½, q = ½
m = np = 500, s = (npq) = 15.81
z = (x - m)/s
z1 = (622.5 - 500)/15.81 = 7.75 and z2
= (623.5 - 500)/15.81 = 7.81
P(623 Heads) = P(7.75 < z < 7.81),
which is almost 0.