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Minchanka [31]
2 years ago
14

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?
Mathematics
1 answer:
alexandr1967 [171]2 years ago
7 0

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 = <u><em>the breaking strength of its most popular porcelain tile</em></u>

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 = <u>0.16</u>

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

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