The shaded area in the following graph indicates the area to the right of x. This area is represented by the probability P(X > x). Normal tables provide the probability between the mean, zero for the standard normal distribution, and a specific value such…
The standard normal distribution is a normal distribution of standardized values called z-scores. A z-score is measured in units of the standard deviation. The mean for the standard normal distribution is zero, and the standard deviation is one. What this does is dramatically simplify the mathematical…
Figure 6.1 If you ask enough people about their shoe size, you will find that your graphed data is shaped like a bell curve and can be described as normally distributed. (credit: modification of work “Shoe shop” by Lo/ Flickr, Public Domain)…
Properties of Continuous Probability Density Functions The probability density function (pdf) is used to describe probabilities for continuous random variables. The area under the density curve between two points corresponds to the probability that the variable falls between those two…
The exponential probability density function is built upon the general exponential function where the variable is an exponent: f(x)=a(b)xf(x)=a(b)x. This equation can be converted to a natural system of logarithms with a base e that has an approximate value of 2.71828.…
The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. When working out problems that have a uniform distribution, be careful to note if the data is inclusive or exclusive of…
The graph of a continuous probability distribution is a curve. Probability is represented by area under the curve. We have already met this concept when we developed relative frequencies with histograms in Descriptive Statistics. The relative area for a range of…
Figure 5.1 The heights of these radish plants are continuous random variables. (credit: modification of work “Radish (Raphanus sativus): White rust caused by Albugo candida” by Scot Nelson/ Flickr, Public Domain) Continuous random variables have many applications. Baseball batting averages, IQ scores,…
Introduction The characteristics of a probability distribution or density function (PDF) are as follows: Hypergeometric Distribution The combinatorial formula can provide the number of unique subsets of size x that can be created from n unique objects to help us…
Another useful probability distribution is the Poisson distribution, or waiting time distribution. This distribution is used to determine how many checkout clerks are needed to keep the waiting time in line to specified levels, how may telephone lines are needed…