Your answers should be rounded to $2$ decimal places:

The following table shows the mesn and variance taken from a set of servor resdings than

can detect defects of

a prociuct.

We need to apply Gaussian classification based on the above information to classify if the

product is clefected or not

The cistribution has the following formuls

$f(x)=\frac{1}{\sqrt[\phantom{2}]{2}}{e}^{-\frac{1}{2}(\frac{x-}{}{)}^2}$

Aesume the defect rate is $10\%$ of all the product

Assume the serspr value is $Z$

A$-$ Find the following assume the resdings in the samples follow the Gaussian

distribution function:

What is good$)$:

Explain why:

$2$ What is P$($test$=0\mathrm{.}5]$defected$)$:

Explain why:

B$-$ We need to make classification of a new sample for a product which has $Z=1\mathrm{.}0$

$1-$ What is $P(gocod|Z=1\mathrm{.}0)$ :

$($ignore the denominatce$)$

Explain why. $[$

$2-$ What is Prdefoct$|Z=1\mathrm{.}0),($ignore the denominator$)$

Explain why:

Besed on the above what is the decision:

a$.$ The product is good

Ob$.$ The product is defected

C$-$ What is the sensor value $x$ such that defected $|Z=x?($in other

words $x$ is on the boundary:

Explain why: $($