Respuesta :
Answer:
16% is the percent of wooden shipping boxes will have breaking strengths greater than 520 pounds per square inch.
Step-by-step 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 [tex]\mu \pm \sigma[/tex]
- About 95% of the data lies within the first two standard deviations that is [tex]\mu \pm 2\sigma[/tex]
- About 99.7% of the data lies within the first three standard deviations that is [tex]\mu \pm 3\sigma[/tex]
We have to find the percent of its wooden shipping boxes that will have breaking strengths greater than 520 pounds per square inch.
Now,
[tex]520 = 500 + 1(20)[/tex]
According to empirical rule around 68% of the data will lie between [tex]500 \pm 1(20)= (480,520)[/tex]
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.
