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L17NormalDistribution

L17NormalDistribution - MGT 2250 — Lesson17 Continuous...

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Unformatted text preview: _ MGT 2250 —- Lesson17, ; Continuous ProbabilityDistributions: The Normal Distribution March 4-, 2011 Deﬁnition: This is the most useful of the continuous probability distributions and has several applications which we will study in the next few weeks. While there are an infinite number of “normal distributions”, they all have the following characteristics in common. 1.) The normal probability density function f - m? /,§;:W \l , j .W.A.WWM.M¥ 6W N 511% D a {i7 QM "xi 2.) The “boll—shaped” curv, Li 7NormalDistrib 3.) Location on the X-axis ‘ V, _ EDETEKﬂMﬁﬂ Q//H /\ >0 ‘ ¥ ‘ E A .x 4.) Shape of the dlstrlbutlo b D ﬁring ‘2 it”? ! WE‘D MﬁATN/ng oﬂ. 5‘54me M5335 [6H r" \ >0“! ﬁwfi , C: *FﬂVTQQ (’T‘c—jg Cpawa M”) Ix) L17N0rmalDistrib ‘f E E 6.) Standard deViati‘ons and areas under the curve b) L17N0rmalDistrib a) Example: A random variable is normally distributed with a mean of 50 and a standard deviation of 5. b) What is the probability the random variable will assume a value between 45 and 55? “M (C? ’2. meé c) What is the probability the random variable will assume a value between 40 and 60? rm 4/” QC? 9 .‘i‘\ ‘2’? c!) What is the probability the random variable will assume a value between 35 and 65? [la/h 7 (3 l i ‘J c) What is the probability the random variable will assume a value iess than 35? w") A 1 ‘ m [3 (Dy ’ I r“ i 6 ‘7 2 3 ~ r U f ? id 3 If g @353; t ,7 p g) e 9“ ’j/“x 2 . /~;::: / UV e-~ L, w M; :2, .3 W? 7; . M ” C . t / E7 L l7N0rmalDistrib ...
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L17NormalDistribution - MGT 2250 — Lesson17 Continuous...

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