Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 261 feet and a standard deviation of 41 feet. Let X be the distance in feet for a fly ball.

a. What is the distribution of X? X ~ N(___,___)

b. Find the probability that a randomly hit fly ball travels less than 336 feet. Round to 4 decimal places. ____

c. Find the 75th percentile for the distribution of distance of fly balls. Round to 2 decimal places. ____ feet

Answer 1

Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
= Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
= Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
Solution: Given that mean = 261, standard deviation = 41

a. X ~ N(261, 41)

b. P((X-mean)/sd < (336-261)/41)
P(Z < 1.8293)
= 0.9664

c. Z = 0.675

X = mean + Z*sigma
= 261 + (0.675*41)
= 288.675
= 288.68