How would you find these probabilities in Excel?

The balanced reinforcement ratio for a singly reinforced concrete beam is given by ACI Standard

$318$ as:

${}_b=0\mathrm{.}85{}_1(\frac{f_c^{\text{'}}}{f_y})(\frac{87,000}{87,000+f_y})$

in which $f_c^{\text{'}}$ and $f_y$ are specified strengths and ${}_1=0\mathrm{.}85($stress block parameter$)$ if $f_c^{\text{'}}4,000$ psi.

Reinforced concrete beams normally are designed to fail by yielding in the reinforcement prior to

crushing of the concrete. Historically, ACl$318$ limited the beam reinforcement ratio, $=\frac{A_s}{b}d$ to

$0\mathrm{.}75{}_b$ to ensure a failure in which the reinforcement yields before the concrete crushes ${?}^1.$

Consider a beam with nominal $f_c^{\text{'}}=4,000$ psi and $f_y=60,000$ psi. The following statistics for in$-$site

concrete and steel strengths would be typical:

${}_{f_c^{\text{'}}}=3,600,{}_{f_c^{\text{'}}}=0\mathrm{.}18$

${}_{f_y}=68,000,{}_{f_y}=0\mathrm{.}11$

Assume that the probability distribution of $f_c^{\text{'}}$ is normal and the distribution of $f_y$ is lognormal$.$ Use

Monte Carlo Simulation $(1,000$ samples$)$ to determine the following:

a$)$ What is the probability that compressive failure occurs $($i$.$e$.$ concrete crushes before

reinforcement yields$)?$ Identify compressive failure as occurring if the actual ${}_b($based on our

understanding of the distribution of $f^{\text{'}}c$ and $fy)$ is less than $0\mathrm{.}75{}_b$ when the nominal fy and

$f^{\text{'}}c$ are used to calculate ${}_b$

b$)$ What limit on the reinforcement ratio should ACl$318$ require to ensure that the probability

of a compression failure is $0\mathrm{.}01$ or less? In other words, what factor needs to be applied to

the nominal ${}_b$ instead of $0\mathrm{.}75$ to keep the probability less than $0\mathrm{.}01?$