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L15Uniform - MGT 2250 —~ Lesson 15 Introduction to...

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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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