Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 257 feet and a standard deviation of 41 feet. Let X be the distance in feet for a fly ball.

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

Find the probability that a randomly hit fly ball travels less than 258 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 = = 257

standard deviation = = 41

(A)X ~ N ( 257, 41)

(B)P(X< 258 ) = P[(X- ) / < ( 258-257) /41 ]

= P(z <0.02 )

Using z table

= 0.5080

probability=0.5080

(C)

Using standard normal table,

P(Z < z) = 85%

= P(Z < z) = 0.85  

= P(Z <1.04 ) = 0.85

z =  1.04 ( Using standard normal z table,)

Using z-score formula  

x= z * +

x= 1.04 *41+257

x= 299.64

x=300