Final answer:
Kelly receives an average of 3 text messages per hour, calculated based on the given average time of 20 minutes between messages and by interpreting this as a Poisson distribution with an average rate of 3 messages per hour.
Step-by-step explanation:
Kelly receives a text message on average every 20 minutes during the daytime. Given that the time between two text messages follows an exponential distribution, and considering that the number of text messages follows a Poisson distribution, we can determine how many text messages Kelly will receive on average during an hour.
To calculate this, we look at the hourly rate. If Kelly receives a text message every 20 minutes, that means Kelly gets 3 messages per hour (since 60 minutes divided by 20 minutes equals 3).
As per the Poisson distribution, the average rate (lambda, λ) is the number of events (text messages) expected to occur within a fixed interval (one hour in this case). Therefore, the mean number of text messages Kelly receives per hour is 3, which is the expected value for our Poisson distribution.