The time of a telephone call (in minutes) to a certain town is a continuous random variable with a probability density function defined by $f(x)=3x^{-4}$ for $[1,\mathrm{\infty })$. Find the probability: $P(x\ge 100)$.
A. 0.000001
B. 0.000074
C. 0.000683
D. 0.000316

Step 1 ：The problem is asking for the probability that the time of a telephone call is greater than or equal to 100 minutes. This is a continuous random variable problem, and we are given the probability density function (pdf) $f(x)=3x^{-4}$ for $x\ge 1$.

Step 2 ：To find the probability $P(x\ge 100)$, we need to integrate the pdf from 100 to infinity. The integral of a pdf over a range gives the probability of the random variable falling within that range.

Step 3 ：The result from the calculation is very close to 0.000001.

Step 4 ：Therefore, the probability that the time of a telephone call is greater than or equal to 100 minutes is approximately 0.000001.

Step 5 ：Final Answer: $\boxed{{\displaystyle 0.000001}}$