Tuna or a Kingfish probability

In summary, the statistician noticed that the masses of the fish he caught could be modeled with a normal distribution, and 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.
  • #1
danago
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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?
 
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  • #2
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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  • #3
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.
 
  • #4
Alright thanks for the help guys :smile:
 

What is the difference between the probability of catching a Tuna and a Kingfish?

The probability of catching a Tuna and a Kingfish depends on various factors such as location, season, and fishing techniques. Generally, Tuna are more abundant and easier to catch compared to Kingfish. However, the probability of catching a larger Kingfish is higher due to their size and strength.

Which one is more likely to be caught, a Tuna or a Kingfish?

As mentioned before, Tuna are more abundant and easier to catch compared to Kingfish. Therefore, the probability of catching a Tuna is higher than that of catching a Kingfish.

Does the size of the fish affect the probability of catching a Tuna or a Kingfish?

The size of the fish does not directly affect the probability of catching a Tuna or a Kingfish. However, larger fish tend to have a higher chance of breaking the fishing line or escaping, which can affect the overall probability of catching them.

Do Tuna and Kingfish have the same probability of being caught in different locations?

No, the probability of catching a Tuna or a Kingfish can vary depending on the location. Different species of Tuna and Kingfish may have different migration patterns and habitats, which can affect the probability of catching them in different locations.

How can I increase the probability of catching either a Tuna or a Kingfish?

To increase the probability of catching a Tuna or a Kingfish, it is important to research and understand their behavior, preferred habitats, and migration patterns. Additionally, using appropriate fishing techniques and equipment, such as using live bait or trolling, can also increase the chances of catching these fish.

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