Question

The most famous geyser 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 eruptions is normally distributed with a standard deviation 21.25 ​minutes,
What is the probability that a randomly selected time interval between eruptions is longer than 94 ​minutes?

Answer 1

To find the probability of a time interval longer than 94 minutes between eruptions, calculate the Z-score using the mean and standard deviation. Look up the cumulative probability associated with the Z-score, and subtract it from 1 to get the desired probability.

Step-by-step explanation:

To find the probability that a randomly selected time interval between eruptions is longer than 94 minutes, we can use the Z-score formula. The Z-score is calculated by subtracting the mean from the given value (94 minutes) and dividing the result by the standard deviation (21.25 minutes). In this case, the Z-score is (94 - 85) / 21.25 = 0.4247.

Next, we look up the cumulative probability associated with the Z-score of 0.4247 in the standard normal distribution table. The cumulative probability is 0.6645.

Finally, subtracting this cumulative probability from 1 gives us the probability that a randomly selected time interval between eruptions is longer than 94 minutes: 1 - 0.6645 = 0.3355, or 33.55%.