Question

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 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

Homework Answers

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%

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