Final answer:
The probability that the study participant selected at random is less than 68 inches tall is approximately 0.4602.
Explanation:
To find this probability, we use the z-score formula for a normal distribution. Given the mean height of 68.4 inches and a standard deviation of 4.0 inches, we calculate the z-score for 68 inches:
\[ z = \frac{68 - 68.4}{4.0} = -0.1 \]
Using a standard normal distribution table or calculator, the cumulative probability corresponding to a z-score of -0.1 is about 0.4602. Thus, the probability that a randomly selected participant is shorter than 68 inches is 0.4602, or 46.02%.
