Question

Suppose you are the CEO of a company that produces sheets of metal that are 1 centimeter thick. This metal is evaluated on the basis of its hardness which is determined by measuring the depth of penetration of a hardened point. Suppose that this depth of penetration is normally distributed with a mean of 1 millimeter and a standard deviation of .02 millimeters.

You are on trial for distributing faulty metal. If the metal is deemed faulty when the depth of penetration is more than 1.3 millimeters, what is the probability you are guilty?

Answer 1

Answer:

0% probability you are guilty

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$, the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 1, \sigma = 0.02$

If the metal is deemed faulty when the depth of penetration is more than 1.3 millimeters, what is the probability you are guilty?

This is 1 subtracted by the pvalue of Z when X = 1.3. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{1.3 - 1}{0.02}$

$Z = 15$

$Z = 15$ has a pvalue of 1

1 - 1 = 0

0% probability you are guilty