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Not a test but a quiz. I've answered all the other questions I just can't figure this out. 

Im just going to stop right here

test?

You are asking us to give you the answer for a test you are taking?

Is your teacher/proctor aware of this?

I'm seeing that 

P[win at home] = 0.2 = 0.8 x 0.25 = P[win] x P[at home]

therefore the two are independent.

are you super sure about this because this a very important test and I am very lost on this question

Although the experimental probability shows that playing at home gives a certain edge, mathematically the events "winning" and playing at home are completely independent since the 2 events are not linked whatsoever. Just take the example of flipping a dye. The probability of getting a Head = 1/2. If after 1000 flips you get a head, the probability of getting a Head on the 1001 flips is always 1/2 (head & tail are independent)

1) 1 and 2 are binomial distributions

3) 1 and 2 are likely to be approximately normally distributed.

Only approximately though as neither ages nor heights can be negative.

The normal distribution, regardless of the mean and variance, has non-zero probability of negative numbers.

...........

Thanks dierdurst for that link.

To "Badada": Look at the link provided above and see where you made the MISTAKE!!.

I suspected that there was a mistake in your 2nd equation, when I suggested that 146 might be 156. But, you didn't check it carefully enough, since now it is quite obvious where the mistake is in that equation.

You have it as: bc + c + c =146 instead of: bc + B + c = 146.

I am always abrupt. Don't take it personally   

Your idea was not unwelcome. It is just that it is important to me that people interact.

Here the actual question asker has not interacted with either of us at all.

That means that the question asker lost interested the minute the question was posted. S/he has probably not read any of this.

It is important that the people who use the forum learn how to put brackets correctly into their questions/answers.

If the asker had been interested enough, they would have learned how to put the brackets in properly.

And then, after that, they would have learn how to answer the question.

If they are always second guessed then they do not learn how to present their work properly.

We often do interpret what people want, which is often different from what the question asks for but there are benefits to not always doing that too.

I was simply pointing that out to you. 

I honestly had not thought of what you said until you said it. It was very observant of you. I expect you do well in maths at school. 

( You probably call it math - That is a give away, I am not American. You (and I) can learn a lot of stuff here, not just maths )

The fact that you are interacting with me now makes you of great value to this forum.

I am very pleased that you are here.   

It would be even better if you became a member. :)

That will be great, thanks :)

Thank you very much for that information! You are right most of you guys teach "brick wall" because when I see most of the people who ask questions they don't say thank you or something :(. I will try my best to respond to people who answer my question and give them a heart and I will try to answer other people questions. Have a great day!