Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 260 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 218 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 = = 260

standard deviation = = 41

a) The distribution of x is normal X ~ N(260, 41)

b) P(x < 218) = P[(x - ) / < (218 - 260) / 41]

= P(z < -1.02)

Using z table,

= 0.1539

c) Using standard normal table,

P(Z < z) = 85%

= P(Z < z) = 0.85  

= P(Z < 1.04) = 0.85

z = 1.04

Using z-score formula,

x = z * +

x = 1.04 * 41 + 260

x = 302.64