Answer :
Using the 68-95-99.7 rule, less than 0.3 percent of values in a normal distribution with a mean of 25 and standard deviation of 3 lie below 16, as it's beyond three standard deviations below the mean.
To determine the percentage of values that lie below 16 in a normal distribution with a mean of 25 and a standard deviation of 3, we use the 68-95-99.7 rule (Empirical Rule). This rule states that approximately 68 percent of the data is within one standard deviation of the mean, 95 percent is within two standard deviations, and 99.7 percent is within three standard deviations.
Since 16 is three standard deviations below the mean (25 - 3*3 = 16), more than 99.7 percent of the values would be expected to lie above 16. Therefore, less than 0.3 percent of the values lie below 16. This figure includes all the values more than three standard deviations below the mean, so the exact percentage below 16 will be somewhat less than 0.3 percent, and for calculation purposes, you may use the standard normal distribution tables or a calculator to find a more precise percentage.
