According to a study conducted by the Department of Pediatrics at the University of California, San Francisco, children who are injured two or more times tend to sustain these injuries during a relatively limited time, usually 1 year or less. If the average number of injuries per year for schoolage children is two, what are the probabilities of these events?

a. A school-age child will sustain two injuries during the year (Use R).

b. A school-age child will sustain two or more injuries during the year (Use R).

c. A school-age child will sustain at most one injury during the year (Use R)

d. Calculate the mean and standard deviation for x, the number of injuries per year sustained by a schoolage child. (Manual Calculation)

e. Within what limits would you expect the number of injuries per year to fall . (Manual Calculation)

Note: For question (a to c), include the R codes and results from within the R environment.