Answer:
45.1%
Explanation:
To find the probability that you will stare at your inbox for less than 6 minutes, we can use the cumulative distribution function (CDF) of the exponential distribution.
The exponential distribution is often used to model the time between events that occur independently at a constant average rate. In this case, the time between emails arriving in your inbox is distributed exponentially with a mean of μ=10 minutes.
The CDF of the exponential distribution is given by the formula: F(x) = 1 - e^(-λx), where λ is the rate parameter of the distribution and x is the value for which we want to calculate the probability.
In this case, since the mean μ=10 minutes, we can find the rate parameter λ by taking the reciprocal of the mean: λ = 1/μ = 1/10 = 0.1.
Now, let's calculate the probability that you will stare at your inbox for less than 6 minutes:
F(6) = 1 - e^(-0.1 * 6) = 1 - e^(-0.6) ≈ 0.451
Therefore, the probability that you will stare at your inbox for less than 6 minutes is approximately 0.451 (rounded to 3 decimal places).
In other words, there is a 45.1% chance that the next email will arrive within 6 minutes after the email you received at 3:00 pm.