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 54 feet.
Use your graphing calculator to answer the following questions. Write your answers in percentform. Round your answers to the nearest tenth of a percent.
a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 216 feet?PP

1. (fewer than 216 feet) = % 0.2129

b) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled more than 234 feet?PP

1. (more than 234 feet) = % 0.6783

Answer 1

Solution :

Given that,

mean = = 259

standard deviation = = 54

a ) P( x < 216 )

P ( x - / ) < ( 216 - 259 / 54)

P ( z < -43 / 54 )

P ( z < -0.80)

= 0.2119

Probability = 0.2119 = 21.19%

b ) P (x > 234 )

= 1 - P (x < 234 )

= 1 - P ( x -  / ) < ( 234 - 259 / 54)

= 1 - P ( z <- 25 / 54 )

= 1 - P ( z < -0.46 )

Using z table

= 1 - 0.3228

= 0.6772

Probability = 0.6772 = 67.72%