Final answer:
Using the Empirical Rule and given that 6.4cm is two standard deviations below the mean for apple diameters, we can conclude that approximately 2.5% of the apples have diameters less than 6.4cm.
Step-by-step explanation:
Using the Empirical Rule, which applies to bell-shaped distributions, we can determine the percentage of apples with diameters less than 6.4cm. First, we calculate how many standard deviations below the mean 6.4cm is. The mean diameter is 7.26cm with a standard deviation of 0.43cm. Subtracting 6.4 from 7.26, we get 0.86cm, which we divide by the standard deviation (0.86cm ÷ 0.43cm) to find that 6.4cm is exactly 2 standard deviations below the mean.
According to the Empirical Rule, approximately 95% of the data is within two standard deviations of the mean. However, since we are looking for the percentage less than 6.4cm, or two standard deviations below the mean, we need to look at the lower half of the distribution. We know that 95% of the data falls within two standard deviations, so 5% is outside this range. Because the data is symmetrically distributed, we can divide this 5% equally between the two tails of the distribution, so each tail has 2.5% of the data. Therefore, approximately 2.5% of the apples have diameters that are less than 6.4cm.