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

According to the 68-95-99.7 rule, approximately 68% of the values are within one standard deviation of the mean, 95% are within two standard deviations of the mean, and 99.7% are within three standard deviations of the mean.

To find the percentage of porcelain tiles with breaking strengths greater than 412.5 pounds per square inch, we need to calculate the z-score of this value:

z = (412.5 - 400) / 12.5 = 1

This means that the breaking strength of 412.5 pounds per square inch is one standard deviation above the mean.

According to the 68-95-99.7 rule, approximately 16% of the values are more than one standard deviation above the mean. Therefore, about 16% of Crosstiles Inc.'s popular porcelain tiles will have breaking strengths greater than 412.5 pounds per square inch. The closest answer choice is C, 16%.

Based on Data Collected from Its Production Processes, Crosstiles Inc