Question

Suppose a geyser has a mean time between eruptions of 83 minutes let the interval of time between the eruptions be normally distributed with the standard deviation 33 minutes what is the probability that a randomly selected time interval between eruptions is longer than 97 minutes

Answer 1

0.336

Explanation:

Here the mean is 83 min and the standard deviation is 33 minutes. Note that

1 standard deviation above the mean comes out to (83 + 33) minutes, or 116 minutes. So 97 minutes is above the mean and below 1 standard deviation above the mean.

What is the probability that the interval is BELOW 97 minutes? If we find this, subtracting it from 1.000 results in the desired probability.

Using the Distribution key on my TI 83 Plus calculator, I get:

normalcdf(-100,97, 83,33) = 0.664.

Subtracting this from 1.000 results in 0.336.

Tthe probability that a randomly selected time interval between eruptions is longer than 97 minutes is thus 0.336.