Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 150 feet and a standard deviation of 55 feet. Let X= distance in feet for a fly ball. In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest 0.01 . (.3) X∼ ( , ) . (.35) For a random fly ball, what is the probability that this ball traveled fewer than 220 feet? P(X<220)= . (.35) The 80th percentile of the distribution of fly balls is given by P(X< )=0.80 .

Answer 1

µ =    150          
σ =    55          
              
P( X ≤    220   ) = P( (X-µ)/σ ≤ (220-150) /55)      
=P(Z ≤   1.273   ) =   0.90   (answer)

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µ=   150                  
σ =    55                  
proportion=   0.8                  
                      
Z value at    0.8   =   0.84   (excel formula =NORMSINV(   0.8   ) )
z=(x-µ)/σ                      
so, X=zσ+µ=   0.84   *   55   +   150  
X   =   196.29   (answer)          

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