According to an nrf survey conducted by bigresearch, the average family spends about $237 on electronics (computers, cell phones, etc.) in back-to-college spending per student. suppose back-to-college family spending on electronics is normally distributed with a standard deviation of $54. if a family of a returning college student is randomly selected, what is the probability that: (a) they spend less than $155 on back-to-college electronics? (b) they spend more than $340 on back-to-college electronics? (c) they spend between $115 and $190 on back-to-college electronics?

Because of the violent nature of the sport, professional american football players are at risk of suffering concussions (or brain injuries) during the violent collisions that occur between players during the game. violent collisions involving hits to the head are particularly risky. suppose the commissioner of the national football league (nfl) institutes a rule requiring players to wear a new, lighter helmet that is designed to reduce head trauma during collisions between players on the field. while the new helmets the probability of a concussion resulting from each individual collision, at the same time the new helmets could also give football players an incentive to play more , which could potentially the amount of violent collisions and thus the number of concussions suffered by nfl players, all else equal.