Final answer:
To find the percentage of values below 21 in a normal distribution with a mean of 25 and a standard deviation of 5, calculate the z-score and consult a Z-table or calculator to find the corresponding percentile, which is expected to be less than 34.1%.
Step-by-step explanation:
The question asks to determine the percentage of values in a normal distribution that fall below a specific value (in this case, 21), given that the distribution has a mean of 25 and a standard deviation of 5. Using the 68-95-99.7 rule (also known as the Empirical Rule) for normal distributions, we know that approximately 68 percent of values lie within one standard deviation of the mean, 95 percent within two standard deviations, and 99.7 percent within three standard deviations.
To find the percentage of values below 21, we first calculate how many standard deviations below the mean this value is: (21 - 25) / 5 = -0.8 standard deviations. Consulting a standard normal (Z-table) or using a calculator for the cumulative distribution function (CDF), we'd find the corresponding percentile for -0.8 standard deviations. Since this is less than one standard deviation away from the mean, we can expect the percentage to be less than 34.1% (which represents half of the 68% within one standard deviation, as the distribution is symmetric about the mean). The exact percentage would commonly be around 21.2%.