Respuesta :
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([tex]\mu=400,\sigma^{2}=12.5^{2}[/tex])
The z score probability distribution for normal distribution is given by;
Z = [tex]\frac{X-\mu}{\sigma}[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = mean breaking strength of porcelain tile = 400 pounds per square inch
[tex]\sigma[/tex] = 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( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{412.5-400}{12.5}[/tex] ) = P(Z > 1) = 1 - P(Z [tex]\leq[/tex] 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.
