EXAMPLE 5.19 Number of Text Messages Sent

Americans aged 18 to 29 years send an average of almost 88 text messages a day.¹¹ Suppose that the number of text messages you send per day follows a Poisson distribution with mean 88. What is the probability that over a week you would send more than 650 text messages?

To answer this using software, we first compute the mean number of text messages sent per week. Since there are seven days in a week, the mean is . Using Excel tells us that there is slightly more than an 8% chance of sending this many texts:

For the Normal approximation, we compute

The approximation is quite accurate, differing from the actual probability by only 0.0021.