A population has a mean of \mu = 100 and

burkinaval1b 2022-01-18 Answered
A population has a mean of μ=100 and a standard deviation of σ=10. If a single score is randomly selected from this population, how much distance, on average, should you find between the score and the population mean?
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Answered 2022-01-18 Author has 38 answers
Average distance of a value form mean is defined as the standard deviation.
a) Average distance =σ=10
b) Average distance of sample mean from population mean = standard error =
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New questions

I recently have this question:
I have a bag of toys. 10% of the toys are balls. 10% of the toys are blue.
If I draw one toy at random, what're the odds I'll draw a blue ball?
One person provided an answer immediately and others suggested that more details were required before an answer could even be considered. But, there was a reason I asked this question the way that I did.
I was thinking about probabilities and I was coming up with a way to ask a more complicated question on math.stackexchange.com. I needed a basic example so I came up with the toys problem I posted here.
I wanted to run it by a friend of mine and I started by asking the above question the same way. When I thought of the problem, it seemed very clear to me that the question was "what is P ( b l u e b a l l )." I thought the calculation was generally accepted to be
P ( b l u e b a l l ) = P ( b l u e ) P ( b a l l )
When I asked my friend, he said, "it's impossible to know without more information." I was baffled because I thought this is what one would call "a priori probability."
I remember taking statistics tests in high school with questions like "if you roll two dice, what're the odds of rolling a 7," "what is the probability of flipping a coin 3 times and getting three heads," or "if you discard one card from the top of the deck, what is the probability that the next card is an ace?"
Then, I met math.stackexchange.com and found that people tend to talk about "fair dice," "fair coins," and "standard decks." I always thought that was pedantic so I tested my theory with the question above and it appears you really need to specify that "the toys are randomly painted blue."
It's clear now that I don't know how to ask a question about probability.
Why do you need to specify that a coin is fair?
Why would a problem like this be "unsolvable?"
If this isn't an example of a priori probability, can you give one or explain why?
Why doesn't the Principle of Indifference allow you to assume that the toys were randomly painted blue?
Why is it that on math tests, you don't have to specify that the coin is fair or ideal but in real life you do?
Why doesn't anybody at the craps table ask, "are these dice fair?"
If this were a casino game that paid out 100 to 1, would you play?
This comment has continued being relevant so I'll put it in the post:
Here's a probability question I found online on a math education site: "A city survey found that 47% of teenagers have a part time job. The same survey found that 78% plan to attend college. If a teenager is chosen at random, what is the probability that the teenager has a part time job and plans to attend college?" If that was on your test, would you answer "none of the above" because you know the coincident rate between part time job holders and kids with college aspirations is probably not negligible or would you answer, "about 37%?"