Based on data collected from its production processes, Crosstiles InC.determines that the Breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a standard deviation of 12.5 pounds per square inch.Based On the 68-95-99.7 Rule, about what percent of its popular porcelain tile will have breaking Strengths greater than 412.5 pounds per square inch?
A)95%
B)68%
C)16%
D)32%
E)47.5%

Question

Quizplus · Accepted Answer

The 68-95-99.7 rule, also known as the empirical rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. A breaking strength of 412.5 pounds per square inch is one standard deviation above the mean (400 + 12.5). Therefore, about 68% of the tiles will have breaking strengths between 387.5 and 412.5 pounds per square inch. Since the distribution is symmetric, 50% of the tiles will have strengths less than the mean, and 34% (half of 68%) will be between the mean and one standard deviation above the mean. Thus, 16% (100% - 50% - 34%) will have breaking strengths greater than 412.5 pounds per square inch.

Based on Data Collected from Its Production Processes, Crosstiles InC