Tuna or a Kingfish probability

[danago]

A statistician went fishing, and noticed that the masses of the fish he caught could be modeled with a normal distribution. He noticed that the Tuna had a mean mass of 22kg, with a standard deviation of 3kg. The Kingfish had a mean of 20kg, and standard deviation of 4kg.

A fish of 22kg is caught; which fish is it more likely to be--A Tuna or a Kingfish?

Well, upon reading the question, i automatically thought the Tuna, since the tuna, on average, are 22kg, and the standard deviation is 3kg, so they are generally closer to their mean than the Kingfish. Is the question really that simple, or should i be looking deeper into it?

 

[kaisxuans]

well the thing is that it can be both. both have a probability that it is 22kg. but if you ask me, i'll say it is the tuna. and if the question is about probability, then is is a 1 in 2 chances for both fishes.
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[HallsofIvy]

Actually, I would think this is a "conditional probability" problem and you would have to know the relative numbers of fish in the area! However, since that information is not given, it looks more like an "estimation of parameters' problem: Given the mean weight of a sample of fish, estimate the true mean weight. The simplest is the maximum likelyhood estimate: which true mean weight gives the highest probability of getting that sample?
Here, the sample is just one fish but obviously, if the true mean weight were 22kg that would make the probability of catching a fish of that weight higher than if you used 20kg as mean weight. Since the "maximum likelyhood estimate" is 22 kg the fish caught is more likely to be a tuna than a kingfish- the obvious answer anyway.

 

[danago]

Alright thanks for the help guys