Question

If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 194 feet

Answer 1

Complete Question

Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 220 feet and a standard deviation of 40 feet. Let X = distance in feet for a fly ball.

If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 194 feet

Answer:

The value is $P(X < 194 ) = 0.25785$

Step-by-step explanation:

From the question we are told that

  The mean is  $\mu = 220 \ feet$

   The standard deviation is  $\sigma = 40 \ feet$

   

Generally the probability that this ball traveled fewer than 194 feet is mathematically represented as

       $P(X < 194 ) = P(\frac{X -\mu}{\sigma } < \frac{194 - 220}{40} )$

Generally   $\frac{X -\mu}{\sigma } = Z (The \ standardized \ value\ of \ X )$

         $P(X < 194 ) = P(Z < -0.65 )$

From the z-table the probability of  $(Z < -0.65 )$

      $P(Z < -0.65 ) = 0.25785$

So  

     $P(X < 194 ) = 0.25785$