Question

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 the 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?

Answer 1

Answer:

16% of its popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch.

Step-by-step explanation:

We are given that the breaking strength of its most popular porcelain tile is normally distributed with a mean of 400 pounds per square inch and a the standard deviation of 12.5 pounds per square inch.

Let X = the breaking strength of its most popular porcelain tile

SO, X ~ Normal($\mu=400,\sigma^{2}=12.5^{2}$)

The z score probability distribution for normal distribution is given by;

                        Z  =  $\frac{X-\mu}{\sigma}$  ~ N(0,1)

where, $\mu$ = mean breaking strength of porcelain tile = 400 pounds per square inch

           $\sigma$ = standard deviation = 12.5 pounds per square inch

Now, probability that the popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch is given by = P(X > 412.5)

        P(X > 412.5) = P( $\frac{X-\mu}{\sigma}$ > $\frac{412.5-400}{12.5}$ ) = P(Z > 1) = 1 - P(Z $\leq$ 1)

                                                               = 1 - 0.84 = 0.16

Therefore, 16% of its popular porcelain tile will have breaking strengths greater than 412.5 pounds per square inch.