Question

Wood shipping boxes are often recommended over cardboard shipping boxes because its strength tends to be higher, therefore, making it more durable and long-lasting. Based on data collected, FedEx determines that the breaking strength of most wooden shipping boxes are normally distributed with a mean of 500 pounds per square inch and a standard deviation of 20 pounds per square inch. Based on the 68-95-99.7 Rule, about what percent of its wooden shipping boxes will have breaking strengths greater than 520 pounds per square inch

Answer 1

16% is the percent of wooden shipping boxes will have breaking strengths greater than 520 pounds per square inch.

Explanation:

We are given the following information:

Mean = 500 pounds

Standard Deviation = 20 pounds

Empirical rule:

• The empirical rule also known as the three-sigma rule or 68-95-99.7 rule
• It is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by σ) of the mean (denoted by µ).
• It shows that 68% falls within the first standard deviation that is
  `\mu \pm \sigma`

• About 95% of the data lies within the first two standard deviations that is
  `\mu \pm 2\sigma`

• About 99.7% of the data lies within the first three standard deviations that is
  `\mu \pm 3\sigma`

We have to find the percent of its wooden shipping boxes that will have breaking strengths greater than 520 pounds per square inch.

Now,

`520 = 500 + 1(20)`

According to empirical rule around 68% of the data will lie between
`500 \pm 1(20)= (480,520)`

Thus, 34% of data lies between 500 and 520.

Data lying above 520 = 50% - 34% = 16%

16% is the percent of wooden shipping boxes will have breaking strengths greater than 520 pounds per square inch.