In a sample of 100 eruptions of the Old Faithful geyser at Yellowstone National Park, the mean interval between eruptions was 101.56 minutes and the standard deviation was 42.69 minutes. A random sample of size 30 is selected from this population. What is the probability that the mean interval between eruptions is between 95 minutes and 110 minutes?

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