8.1 Continuous Probability Distributions

Binomial probability distribution and hypergeometric distribution deal with discrete data.
Possible values of the random variable are natural numbers, because they arise from counting processes (usually successful) or unsuccessful trials.
A distribution which is not symmetricmay be positively skewed(tail pulled to the right) Negatively skewed (tail pulled to the left) *Both kinds of skewed distributions are unimodal.

*A distribution with two humps is called a bimodal. This distribution may occur when a population consists of two groups with different attributies.
Ex.Distribution of adult shoe sizes is bimodal because men tend to have bigger feet then women.

MOdelling Distributions with Equations

You want to find the probabilty that a variable falls in a particular range of values.This kind of probability can be determined from the area under the distribution curve. The curve represents the PROBABILITY DENSITY the probabilty per unit of the continuious variable.

Exponential distribution predicts the waiting t6imes between consecutive events in any rondom sequence of events. The equation for this distribution is
Y=Ke^ke
*the longer the average weight the smaller the value Kand the morethe graph slopes down.

Continuious probability distributions allow for fractional or decimal values of the random variable.
Distributions can be represented by a relative frequency table, a graph, or an equation.
Probabilities can be computed by finding the area under the curve within the appropriate interval.

Ex.#1Probabilities in a uniform distribution.
The driving time between Toronto and North Bay is found to range evenly between 195 and 240 mins . What is the probability that the drive will take more then 210 mins.

SOLUTION:
The time distribution is uniform, which means that every time in the range is equally likely . The graph will be a horizontal straight line. The total area under this line must equal because all the possible driving times lie in the range 195 to 240 mins.

therefor:the height of the line is 1divided by 240-195=0.022
P(driving time < 210)=0.022x(210-195)=0.33

By: maria Boraczuk & Daniella

Comment:
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