To find the probability that a fly ball travels fewer than 220 feet in a normally distributed setting, we need to standardize the score using the z-score formula.
The formula for the z-score is:
\[ z = \frac{(X - \mu)}{\sigma} \]
where:
- \(X\) is the value for which we are finding the probability (220 feet),
- \(\mu\) is the mean (250 feet),
- \(\sigma\) is the standard deviation (50 feet).
Substituting the values into the formula:
\[ z = \frac{(220 - 250)}{50} = \frac{-30}{50} = -0.6 \]
Now we need to find the probability that \(Z\) (the standard normal variable) is less than -0.6. This can be found using the standard normal distribution table or a calculator.
Looking up the z-value of -0.6, we find:
\[ P(Z < -0.6) \approx 0.2743 \]
Thus, the probability that a randomly chosen fly ball traveled fewer than 220 feet is approximately:
\[ \boxed{0.2743} \]