## To calculate the probability that there are fewer than 100 accidents at the intersection in a year, we need to restate the event in terms of x-bar (the mean number of accidents per week) minus the mean number of accidents per week.

Let's call the mean number of accidents per week "Î¼" and the standard deviation of the yearly average "Ïƒ/âˆš52" (where Ïƒ is the original standard deviation).

Now, we can use the standard normal distribution to calculate the probability:

P(x-bar < 100/52) = P((x-bar - Î¼) / (Ïƒ/âˆš52) < (100/52 - Î¼) / (Ïƒ/âˆš52))

By substituting the values of Î¼ and Ïƒ, we can calculate the probability using the standard normal distribution table or statistical software.