Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 259 feet and a standard deviation of 37 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 338 feet. Round to 4 decimal places. c. Find the 85th percentile for the distribution of distance of fly balls. Round to 2 decimal places. feet

Answer 1

Solution :

Given that ,

mean = = 259

standard deviation = = 37

a. X ~ N(259 , 37)

b. P(x < 338)

= P[(x - ) / < (338 - 259) / 37]

= P(z < 2.14)

Using z table,

= 0.9838

Probability = 0.9838

c. The z-distribution of the 85% is,

P(Z < z) = 85%

= P(Z < z ) = 0.85

= P(Z < 1.036 ) = 0.85

z = 1.036

Using z-score formula,

x = z * +

x = 1.036 * 37 + 259

x = 297.332

Answer = 297.33 feet.