Question

Problem 2 Suppose that the distance of fly balls hit to the outfeld (in baseball) is normally distributed with a mean of 251 feet and a standard deviation of 59 feet. We randomly sample 38 fly balls Let X average distance in fet for 38 fly balls Enter numbers as integers or fractions in "p/a" form, or as decimals accurate to nearest 0.01 a. (20) Xeick one) b. (20) Use the mean and standard deviation of X to determine the z value for X 240 c (20) Illustrate P(X > 240) as an area by adjusting the slider along the horizontal axis to control the z value 0.00 0.300 02 0.1

Answer 1

a) here std deviation of mean =59/sqrt(38)=9.57

hence X ~ N(251 ,9.57)

b z =(Xbar-mean)/std deviation=(240-251)/9.57=-1.15

c)move the pointer to z=-1.15

d)

P(Xbar>-1.15)=0.8749

e)

80 th percentile z score =0.84

hence x =251+0.84*9.57=259.04