Question

Use the Empirical Rule %to answer each question. During 1 week an overnight delivery company found that the weights of its parcels were normally distributed, with a mean of 28 ounces and a standard deviation of 7 ounces. What percent of the parcels weighed between 14 ounces and 35 ounces? (Round your answer to one decimal place.)

Answer 1

The Empirical Rule states that approximately 68% of the data falls within one standard deviation of the mean. In this case, approximately 68% of the parcels weigh between 14 ounces and 35 ounces.

Step-by-step explanation:

To answer this question, we can use the Empirical Rule, also known as the 68-95-99.7 Rule, which states that for a normal distribution:

• Approximately 68% of the data falls within one standard deviation of the mean.
• Approximately 95% of the data falls within two standard deviations of the mean.
• Approximately 99.7% of the data falls within three standard deviations of the mean.

In this case, the mean weight of the parcels is 28 ounces and the standard deviation is 7 ounces. We are interested in the percentage of parcels that weigh between 14 ounces and 35 ounces, which is within one standard deviation of the mean. Since one standard deviation from the mean is 7 ounces, and 35 ounces is one standard deviation above the mean, we can conclude that approximately 68% of the parcels weigh between 14 ounces and 35 ounces.