Final answer:
The empirical rule can be used to answer questions about the percentage of data within certain ranges in a normal distribution. For the given question, approximately 68% of the parcels weigh between 8 ounces and 20 ounces, and approximately 5% of the parcels weigh more than 28 ounces.
Step-by-step explanation:
To answer part (a) of the question, we can use the empirical rule. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations of the mean, and 99.7% falls within three standard deviations of the mean.
In this case, the mean weight of the parcels is 16 ounces with a standard deviation of 4 ounces. Therefore, the range between 1 standard deviation below the mean and 1 standard deviation above the mean represents approximately 68% of the parcels. This would be from 16 - 4 = 12 ounces to 16 + 4 = 20 ounces. So, approximately 68% of the parcels weigh between 8 ounces and 20 ounces.
To answer part (b) of the question, we need to find the percentage of parcels that weigh more than 28 ounces. Using the empirical rule, we know that approximately 95% of the parcels fall within two standard deviations of the mean. So, the range between 2 standard deviations above the mean and infinity represents approximately 5% of the parcels. In this case, that range is from 16 + 2(4) = 24 ounces to infinity. Therefore, approximately 5% of the parcels weigh more than 28 ounces.