Final answer:
To find the probability that your favorite celebrity does not post any messages for any random day, we can use the Poisson distribution. The probability is approximately 0.111.
Step-by-step explanation:
To find the probability that your favorite celebrity does not post any messages for any random day, we can use the Poisson distribution. The Poisson distribution is a probability distribution that models the number of events that occur in a fixed interval of time or space.
In this case, the average number of messages your favorite celebrity posts per day is 2.2. Since the Poisson distribution measures the number of events in a fixed interval, we can treat each day as a separate interval.
The probability of not posting any messages in a day can be calculated using the formula:
P(X = 0) = (e^-λ * λ^0) / 0!
where λ is the average number of events in the interval. In our case, λ = 2.2.
Plugging in the values into the formula:
P(X = 0) = (e^-2.2 * 2.2^0) / 0!
Simplifying further:
P(X = 0) = e^-2.2
Calculating this using a calculator, we get:
P(X = 0) ≈ 0.111
Rounded to three decimal places, the probability that your favorite celebrity does not post any messages for any random day is approximately 0.111.