Problem 6.13 An artillery shell is fired at a target. The distance (in meters) from the point of impact to the target is modeled by the random variable 7.22χ2 2. If the shell hits within 10 meters of its target it is destroyed.

(a) Find the probability that the target is destroyed by the shell.

(b) If shells are fired repeatedly, how many rounds are required to ensure a 90% probability of destroying the target? Note: The decision of how many shells to fire must be made ahead of time, since we cannot see whether we have hit the target.