Chapter 7 Definitions
1) Continuous Probability Distribution: These describe probabilities associated
with random variables that are able to assume any of an infinite number of values
along an interval.
2) Probability Density Function: Refers to the vertical coordinate which is a
function of x, described as f(x).
3) Normal Distribution: The most important continuous distribution in statistics
which occupies this position for three key reasons. 1) many natural and economic
phenomena tend to be approximately normally distributed; 2) It can be used in
approximating other distributions, including the binomial; 3) Sample means and
proportions tend to be normally distributed whenever repeated samples are taken
forma given population of any shape.
4) Areas Beneath the Curve:
 About 68.3% of the area is in the interval µ - σ to µ + σ.
 About 95.5% of the area is in the interval µ - 2σ to µ + 2σ.
 Nearly all of the area (about 99.7%) is in the interval µ - 3σ to µ + 3σ.
χ−µ
5) The z-score for a standard normal distribution: z = ————
σ
6) The Standard Normal Distribution Table: Regardless of the units involved
(e.g., pounds, hours, dollars, and so on) in the original normal distribution, the
standard distribution converts them into standard deviation distances from the
mean.
7) The Bernoulli Process: The binomial distribution assumes a Bernoulli process,
which has the following characteristics: 1) There are two or more consecutive
trials; 2) On each trial, there are just two possible outcomes-denoted as “success”
or “failure”; 3) The trials are statistically independent; that is, the outcome in any
trial is not affected by the outcomes of earlier trials, and it does not affect the
outcomes of later trials; 4) The probability of a success remains the same from
one trial to the next. This is satisfied if we either sample with replacement or the
sample is small compared to the size of the population.
8) The Mean and Standard Deviation of the Binomial Distribution: The basis for
the normal distribution that will be used in making the approximation.
9) Correction for Continuity: This correction consists of expanding each possible
value of the discrete variable, x, by 0.5 in each direction.
10) The Approximation Procedure: Demonstrates the use of the normal distribution
to approximate the binomial. It represents a situation in which both nπ and n(1 –
π) are ≥5, which is requisite for using the approximation.
11) Exponential Distribution: Describes the continuous random variable, x = the
amount of time, space, or distance between occurrences of these rare events.
 For χ = the length of the interval between occurrences:
f(χ) = λe^-λχ for χ>0 and λ>0. Where λ = the mean and variance of a
Poisson distribution. 1/λ = the mean and standard deviation of the

corresponding exponential distribution, and e = the mathematical constant,
2.171828, the base of the natural logarithm system.
Areas beneath the curve: P( χ≥k) = e^-λk, where k =the time, space, or
distance until the next occurrence.