$2$

CE $372$ Summer $2024$

Risk Analysis in CEE

Name $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Homework #$3(20$ pts$)$

PID Number$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Always show your work in each problem for partial credits

$1$ of $2$

Steel cable is "rated" at a yield strength of $36\mathrm{.}0$ ksi. We are pretty sure the real strength of a

cable will be at least this much $($Hint: for problems $1$ and $2).$

$1.(6$ pts$)$ Over a long time, cable from Acme Cable Co$.$ has a mean strength $$x of $37\mathrm{.}5$ ksi with a

known $($population$)$ standard deviation of $1$ ksi. Find the probability that a random piece of the

cable has a strength x lower than $36\mathrm{.}0$ ksi

Pr $($x $<36\mathrm{.}0)=\_\_\_\_\_\_\_\_\_\_\_\_$

$2.(10$ pts$)$ You buy five random samples of cable from another manufacturer, Cheatum Cable,

and find that your sample mean is $36\mathrm{.}6$ ksi with a sample standard deviation of $0\mathrm{.}45$ ksi. At the

$95\%$ confidence level, you want to know if the mean strength of Cheatum Cables is greater than

$36\mathrm{.}0$ ksi.

tcalc $=\_\_\_\_\_\_\_\_\_\_\_\_$

tcrit $=\_\_\_\_\_\_\_\_\_\_\_\_$

Do you accept or reject the null hypothesis? $\_\_\_\_\_\_\_\_\_\_$

As a result, what can you say? $($One sentence in words$)$

CE $372$ Summer $2024$

Risk Analysis in CEE

Name $\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Homework #$3(20$ pts$)$

PID Number$\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_$

Always show your work in each problem for partial credits

$2$ of $2$

$3.(2$ pts$)$ Did the answers to problems $1$ and $2$ give you enough information to decide which

cable $($Acme Cable Co$.$ vs$.$ Cheatum Cables$)$ is "better"? If yes, which is better; if not, why not?

$4.(1$ pt$)$ In a paired t$-$test, what is the expected mean of the differences? $\_\_\_\_\_\_\_\_\_\_\_\_\_$

$5.(1$ pt$)$ We are planning to calculate the probability of having a $10-$year flood in $48$ months.

What is the value of $$t$?$

$$t $=\_\_\_\_\_\_\_\_\_\_\_\_\_\_$