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1. It is given that Y ∼ N(33, 21). Find the value of a given that P(33 − a < Y < 33 + a) = 0.5.?

Please explain thoroughly. I do not get it , any kind of help would be great
2. (Original post by Sammysammy99)
It is given that Y ∼ N(33, 21). Find the value of a given that P(33 − a < Y < 33 + a) = 0.5.?

Please explain thoroughly. I do not get it , any kind of help would be great
First of all, draw a nice sketch of the normal distribution for Y, marking on the mean.

You should notice that the region is actually symmetrical about the mean, which means that the probabilities and are indeed the same.

This means we only need to focus on one of them if we can.
Indeed we can because know that

This implies that we have .

We can also rewrite the LHS by saying that hence we have hence

From here it should be straight-forward to determine such that holds.
3. (Original post by RDKGames)
First of all, draw a nice sketch of the normal distribution for Y, marking on the mean.

You should notice that the region is actually symmetrical about the mean, which means that the probabilities and are indeed the same. This means we only need to focus on one of them if we can.
Indeed we can because know that

This implies that we have . We can also rewrite the LHS by saying that hence we have hence

From here it should be straight-forward to determine such that holds.
Thank you very much , I really appreciate all that , I get it , but the only question is that is p(y<33) equal to 0.5? Thank u again , really helpful
4. (Original post by Sammysammy99)
Thank you very much , I really appreciate all that , I get it , but the only question is that is p(y<33) equal to 0.5? Thank u again , really helpful
Because 33 is the mean, and in normal distribution the mean=mode=median.
5. (Original post by Sammysammy99)
Thank you very much , I really appreciate all that , I get it , but the only question is that is p(y<33) equal to 0.5? Thank u again , really helpful
Because 33 is the mean, and we know that normal distribution is symmetrical about the mean which means that the probability is 50% on either side of the mean.
Because 33 is the mean, and in normal distribution the mean=mode=median.
I just meant where did u get the 0.5 from
7. (Original post by Sammysammy99)
I just meant where did u get the 0.5 from
From the 50% I'm talking about.
8. (Original post by Sammysammy99)
I just meant where did u get the 0.5 from
Think about the shape of the distribution. It is symmetrical about the mean with 0 skew, hence the P(X>33)=P(X<33)=0.5
9. (Original post by RDKGames)
First of all, draw a nice sketch of the normal distribution for Y, marking on the mean.

You should notice that the region is actually symmetrical about the mean, which means that the probabilities and are indeed the same.

This means we only need to focus on one of them if we can.
Indeed we can because know that

This implies that we have .

We can also rewrite the LHS by saying that hence we have hence

From here it should be straight-forward to determine such that holds.
Alright thank you very muchhhhh I get it now!!!

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