Question

g Steel used for water pipelines is often coated on the inside with cement mortar to prevent corrosion. In a study of the mortar coatings of the pipeline used in a water transmission project in California, researchers noted that the mortar thickness was specified to be 7/16 inch. A very large sample of thickness measurements produced a mean equal to 0.635 inch and astandard deviation equal to 0.082 inch. If the thickness measurements were normally distributed, approximately what proportion were less than 7/16 inch?

Answer 1

Answer:

$P(X$

And we can find this probability using the z table and we got:

$P(z$

Step-by-step explanation:

Let X the random variable that represent the thickness of a population, and for this case we know the distribution for X is given by:

$X \sim N(0.635,0.082)$  

Where $\mu=0.635$ and $\sigma=0.032$

We are interested on this probability

$P(X$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(X$

And we can find this probability using the z table and we got:

$P(z$