normal distribution problem: conditional probability

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Mar 26th 2011, 02:21 PM
Evan.Kimia

normal distribution problem: conditional probability

If X is N(75,100), compute the conditional probability P(PX>85|X>80)

I use the theorem sigma((b-mean)/standard deviation)-sigma((a-mean)/standard deviation) and a normal distribution probability table to get these probabilities:

.8413 for X > 85
and
.6915 for X > 80.

I see the probability of an event A given an event B has occurred is

P(A|B)=P(A union B)/P(B)

how could i find P(A union B) so i can apply this formula? Thanks!
Mar 26th 2011, 02:34 PM
Plato

Quote:

Originally Posted by Evan.Kimia

If X is N(75,100), compute the conditional probability P(PX>85|X>80)
P(A|B)=P(A union B)/P(B)

how could i find P(A union B) so i can apply this formula? Thanks!

It is not union. It is intersection.

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}$

Hint $(X>85)\cap(X>80)=(X>85)$
Mar 26th 2011, 02:43 PM
Evan.Kimia

if I understand Plato correctly (which i probably didnt) , P(A∩B) where in this case P(A)=.8413 and P(B)=.6915, would be equal to P(A).

but that would mean .8413/.6915 which doesnt give me the correct answer. (answer in the back of the book is .514)

What am i missing? Thank ya.
Mar 26th 2011, 03:05 PM
Plato

Quote:

Originally Posted by Evan.Kimia

if I understand Plato correctly (which i probably didnt) , P(A∩B) where in this case P(A)=.8413 and P(B)=.6915, would be equal to P(A).

but that would mean .8413/.6915 which doesnt give me the correct answer. (answer in the back of the book is .514)

What am i missing? Thank ya.

I don't know what you are missing.
I do know that I do not get those same numbers.
I do know that the answer to the question you posted is $\dfrac{P(X>85)}{P(X>80)}$ .

Post script: Now I do get your textbook's answer.
I was not use to the notation you are using.
i.e. $\sigma=10$
Mar 27th 2011, 07:26 PM
Evan.Kimia

I also somehow got the wrong values out of the table for P(A) and P(B) so you were correct after all. Thanks again!