Question

In: Statistics and Probability

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed...

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

Solutions

Expert Solution

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


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