Question

The most famous peyser in the world, Old Faithful in Yellowstone National Park, has a mean time between eruptions of 85 minutes. If the interval of time between the eruptio with standard deviation 21.25 minutes, complete parts (a) through (1)

(a) What is the probability that a randomly selected time interval between eruptions is longer than 95 minutes?
The probability that a randomly selected time interval is longer than 95 minutes is approximately 0.3102 (Round to four decimal places as needed)

Answer 1

To find the probability that a randomly selected time interval between eruptions is longer than 95 minutes, we can use the Normal Distribution. The probability is approximately 0.6802 or 68.02%.

Step-by-step explanation:

To find the probability that a randomly selected time interval between eruptions is longer than 95 minutes, we can use the Normal Distribution. First, we need to standardize the value of 95 minutes using the formula z = (x - mean) / standard deviation, where x is the given value, mean is the mean time between eruptions, and standard deviation is the standard deviation of the time between eruptions. Plugging in the values, we get z = (95 - 85) / 21.25 = 0.4706. Now, using a standard normal distribution table or a calculator, we can find the probability associated with z = 0.4706, which is approximately 0.3198. However, we are interested in the probability that the time interval is longer than 95 minutes, so we need to subtract this probability from 1. Therefore, the probability that a randomly selected time interval between eruptions is longer than 95 minutes is approximately 1 - 0.3198 = 0.6802, or approximately 0.6802 or 68.02%.