Determine whether the finite correction factor should be used. If$$ so$,$ use it in your calculations when you find the probability.

In a sample of $100$ eruptions of the Old Faithful geyser at Yellowstone National$$ Park, the mean interval between eruptions was $129\mathrm{.}58$ minutes and the standard deviation was $108\mathrm{.}53$ minutes. A random sample of size $30$ is selected from this population. What is the probability that the mean interval between eruptions is between $121$ minutes and $140$minutes$?$