Final answer:
In a normal distribution, approximately 16% of the scores are lower than one standard deviation below the mean. This is based on the Empirical Rule, which indicates that 68% of values are within one standard deviation of the mean, with 34% on each side of the mean.
Step-by-step explanation:
In a normal curve, the percentage of the scores that fall lower than one standard deviation below the mean is approximately 16%. This result comes from the Empirical Rule or the 68-95-99.7% rule which states that in a symmetric bell-shaped distribution, about 68% of the values lay within one standard deviation of the mean, approximately 95% within two standard deviations, and over 99% within three standard deviations.
Knowing that 68% of values lie within one standard deviation on both sides of the mean, we can determine the amount on each side by dividing it in half, which gives us 34%. Therefore, to find the percentage below one standard deviation from the mean, we take the halfway point (50%) and subtract 34%, arriving at approximately 16%. This proportion is useful in fields like psychology and education, specifically in evaluating IQ scores, where an IQ of 85 would be described as 'one standard deviation below the mean' of 100.