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University of Toronto Mississauga

Communication, Culture and Technology

CCT226H5

Lee Bailey

Fall

Description

Chapter 6
In this chapter we study continuous probability distributions. A continuous probability results from measuring something. Like distance from the residence
to the classroom, the weight of an individual, the amount of bonuses earned by CFOs. When examining continuous distribution we are interested in
information such as the percent of students who travel less than 10km or the percent of students who travel more than 8km. In other words, for a
continuous distribution, we may wish to know the percent of observations that occur within a certain range. It is important to realize that a continuous
random variable has an infinite number of values within a particular range.
There are two families of continuous probability distributions, the uniform probability distribution and the normal probability distribution. These describe
the likelihood that a continuous random variable that has an infinite number of possible values will fall within a specified range.
The family of uniform probability distributions
• This is rectangular in shape and is defined by minimum and maximum values
• An example of this: buses run every 20 minutes. Students arrive at the bus stop at random times to catch the next bus. The random variable is the
number of minutes a student waits for the next bus, and it can assume any value between 0 and 20.
• The mean of a uniform distribution is located n the middle of the interval between the min and max values
a+b
• Therefore the mean is µ =2
• The standard deviation describes the dispersion of a distribution. In this one, the standard deviation is also related to the interval between the max
(b−a) 2
and min values. σ=
√ 12
• A and B values are the max and min. B is the max, A is the min.
1
• Equation of uniform distribution is:b−ax) =
• The rectangular shape of this distribution allows us to apply the area formula for a rectangle. We find the area by multiplying the area of a rectangle
by multiplying the length by height.
The Family of Normal Probability Distributions
• This one is bell shaped. The arithmetic mean, median and mode are equal and located in the centre of the distribution. The total area under the
curve is 1.00. Half the area under the curve is to the right from the centre point, and the other half is to the left.
• It’s symmetrical. It we cut the curve vertically at the center, they will be mirror images
• The distribution is asymptotic; the curve gets closer and closer to x-axis but never touches it.
• LOOK ON PAGE 178
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