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Unformatted text preview: MGT 2250 —~ Lesson 15
Introduction to Continuous Probability Distributions:
The Uniform Probability Distribution ’
June 23, 2011 ' Deﬁnition: A continuous probability distribution describes the distribution of all possible intervals of
values a continuous random variable can assume and the probability of a value falling
Within that interval. These are represented by a probability “curve” that is deﬁned by a
probability density function. Probabilities for these functions are determined by areas ' under the curve between two points (a specified interval) and the probability of any ONE
point is “'0”. The total area under the curve will be equal to "‘1". Uniform Probability Distribution This is the simplest of all the continuous probability distributions and has the
following characteristics: 1) It is only defined between two specified points (Le. it is a finite
distribution, “closed” at two ends.)
2) The probabilities are distributed uniformly between these two specified points. The probability of any values falling beyond these
two points is zero.
3) The “curve" is a rectangle.
The uniform probability density function: ﬁt #61 tVéQ/O 5m The expected value and standard deviation ofa uniform probability
distribution: (M . (”A «C
11" 5‘24: Cid! Q a2 ”'72, Example: Delta Airlines quotes a ﬂight time from Atlanta to Savannah
of 43 minutes. Assuming these flight times are uniformly distributed
between 40 and 50 minutes: 3) Write out and graph the uniform probability function for these
ﬂight times. l S 0x} 2» {3'40 k/MWW ,.
CtVVD {0 9313/ b) What is the probability a flight will take between 43 and 47 minutes? 9(agi’7ljﬁéj :3 (bell) (gee!) I C) What is the probability a flight will be late based on Delta’s
quoted ﬂight time? f” 
age «WC»? (‘7) 6’?) d) What is the expected value and sdeMeviatieWthis distribution?
E (v) '2 ‘: 119/
L. e) If Delta accepts a flight time between 41 and‘ 45 minutes to be
“acceptable”, What is the probability a ﬂight will be!
“unacceptable” according to Delta s standard? pfawx Iv} & (be!) /2!« f) What is the probability a ﬂight will take more than 50 minutes? ...
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 Summer '08
 Milne

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