Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 240 feet and a standard deviation of 42 feet. Let x distance in feet for a fly ball. Part() Give the distribution of X X-N 240 Part() Ionely balls randomly chosen from this wibor, what is the probability that this ball traveled fewer than 180 feet? (Round your answer to four decimal places) Sketch the graph L. 300 100 X 100 200 400 10 300 400 Part (0) Find the oth percentile of the distribution of ty bals. (Round your answer to one decimal place.) 11 Sketch the graph 100 200 wine the probability statement. (Lot represent the score that corresponds to the com percenti) PX)

Answer 1

Qulance feet for a fly ball XN N(462) M 240 6 = 42 a) XNN ( 240, 422) XN N (240, 1964) b) P(x > 186)= 18 6-1) X-4 > ' ( PlZy 186 -240 42 27240) -Pl z> -1.2857) = 10.90 from ZNN1011) Normal Table Third paut es correct 100 200 300 400 soth percentile P[ Xsx]=0.80 نا 2 x 4 0.80 2-4 3-0 -080 P[ 2 < x-240 Also from Table, P[ 28 0.842] = 0.80 x 275.364 80 x-240 = 0:842 72 Percentile Soth is 275.364 Peobabilely slateement U of X<]20-80 200 300 400