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To celebrate their 30th birthday, brothers Mario and Luigi of the Nintendo Mario video game franchise wish to study the distribution of heights of their mushroom enemies, the Goombas. Their reasoning is that shorter Goombas are easier to jump on. (Goombas die when Mario and Luigi jump on them.)
(a) If we assume that the population of Goomba heights are normally distributed with mean 12 inches and standard deviation 6 inches, what is the probability that a randomly chosen goomba has a height between 13 and 15 inches?
(b) Koopa Troopas, other enemies of Mario & Luigi, have normally distributed heights with mean 15 inches and standard deviation 3 inches. What is the probability that a randomly chosen Koopa Troopa is taller than 75% of Goombas?
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