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# Pg 47 - a ﬁpm’hé-d*F[x>w\l‘*l"fl/X<>l...

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Unformatted text preview: a ﬁpm’hé-d *F[x>w\l‘*l"fl/X<>;l ‘P(xzé)(<.>y):--nyax.} Hing.) 22 Normal Distribution (333.129.433.11 .0 The Normal Distribution is one of the most important distributions in statistits, it is used to model physical characteristics, measurements, measurement errors, and other physical phenomenon. Even when the underlying data. is not normally distiibuted sums gmd averages may b£3. Let X be a normal Iandom vasiable with paranuters [L if?!” 13ml {72 ,NX NW, G2). The pdf of X is given by 5\$§W>Qﬂmd f( )~ 1 {Hf-1 W3 (Malian ””2 o The mean is ,u and the variance is :72 In Suppose XN NNLo 02) Z w —"5 and ZN N6) 1) We can use Z values to ﬁnd any probability for X by standardization using the Z table. 0 Example: Toby is 8 years old and enjoys hauling barbi dolls, GI. Joe vehicles, and train sets for his friends in the neighborhood. His parents have determined that he travels an average of ”5'0 feet per day with a. standard deviation of 20 feet. 625?? X» f )1) (a) “That is the probability Toby travels less than 25 feet in a day? :jb {\H) J? X 'Ul’ﬁiiar‘tr (lee/l )(m 22/(70)20) was): die/”23 £5705) Péze 2 val—.0122 (b) What is the probability Toby travels betWeen 50 and 100 feet per day? FLEOéXQoa? *‘“> ﬁhir x ..... Finlaf) :: PLZ< 115630 -2PLZ< 5—25 3332“ .l 5‘57: .77ng (o) What IS the probability Toby travels more than 75 for: per (luv? 75 00>? ' Myﬁg) Fflk £75) ‘~ I f Z 472 _, :1._P(7<Q15):/~.56l%?0 :: .VOE 47 ...
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