Suppose that $\mathrm{X}$ is a random variable with the binomial distribution with $n=18$ and $p=0.8453$. Calculate $P(X=14)$. If rounding is necessary, round as indicated on the formula sheet.

Step 1 ：We are given that $\mathrm{X}$ is a random variable with the binomial distribution with $n=18$ and $p=0.8453$. We are asked to calculate $P(X=14)$.

Step 2 ：The binomial distribution is given by the formula: $P(X=k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k}$, where $n$ is the number of trials, $k$ is the number of successes, $p$ is the probability of success on each trial, and $\binom{n}{k}$ is the binomial coefficient, which can be calculated as $\frac{n!}{k!(n-k)!}$.

Step 3 ：Substitute $n=18$, $k=14$, and $p=0.8453$ into the formula to calculate $P(X=14)$.

Step 4 ：Calculate the binomial coefficient $\binom{n}{k}$: $\binom{18}{14} = 3060.0$.

Step 5 ：Substitute the binomial coefficient and the given values into the formula: $P(X=14) = 3060.0 \cdot 0.8453^{14} \cdot (1-0.8453)^{18-14}$.

Step 6 ：Solve the equation to get the probability: $P(X=14) = 0.16666133140213757$.

Step 7 ：Round the result to four decimal places: $P(X=14) \approx 0.1667$.

Step 8 ：Final Answer: The probability $P(X=14)$ is approximately \(\boxed{0.1667}\).