EXAMPLE 5.33

Number of snaps received. In Example 5.11, it was reported that Snapchat has more than 100 million daily users who send over 400 million snaps a day. Suppose that the number of snaps you receive per day follows a Poisson distribution with mean 12. What is the probability that, over a week, you would receive more than 100 snaps?

To answer this using software, we first compute the mean number of snaps sent per week. Because there are seven days in a week, the mean is Plugging this into R tells us that there is slightly less than an 4% chance of receiving this many snaps:

For the Normal approximation we compute

The approximation is quite accurate, differing from the actual probability by only 0.0012.