Final answer:
To determine the probability that a participant is under 66 inches tall, calculate the z-score using the formula (X - μ) / σ, which for this example equates to -0.7333. The corresponding probability is approximately 23.17%.
Step-by-step explanation:
To find the probability that a study participant has a height that is less than 66 inches, we need to calculate the z-score and then use the standard normal distribution table (or a calculator) to find the corresponding probability. The z-score formula is:
z = (X - μ) / σ
Where X is the value we are looking at (66 inches), μ is the mean (68.2 inches), and σ is the standard deviation (3.0 inches).
First, calculate the z-score:
z = (66 - 68.2) / 3.0
z = -2.2 / 3.0
z = -0.7333
Next, look up the z-score in the standard normal distribution table to find the probability that the z-score is less than -0.7333. This value is approximately 0.2317.
Therefore, the probability that a study participant has a height that is less than 66 inches is 0.2317, or 23.17%.