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# S1 Normal Distributions Watch

1. I have a concept issue i guess. If they say P(X>174) = 30% and P(X<154) = 5%, find mean and Standard deviation, isn't the 174 from P(X>174) suppose to be LESS than the mean? I need to understand when the variable is less than the mean or greater than to understand the graph of which ill be drawing. Also when they ask for questions such as P(w<x<174), we solve it both ways right? Like P(w-u/SD<x<174-u/sd) this i guess? GHSomeone help?
2. (Original post by Warfare)
isn't the 174 from P(X>174) suppose to be LESS than the mean?

I do not understand your issue

You simply have 2 simultaneous equestions
3. As in while im drawing the diagram will 174 be before the mean or after the mean?
4. Well, given that P(X>174) = 0.3

Where do you think it will be

BTW ... good to hear that you are drawing a diagram
5. I think its suppose to be less than the mean, but i am suppose to be wrong as its actually above the mean. I dont get why. Isnt 0.30 < 0.50 and thats less the mean - thats why 174 will be before the mean?
Yeah i always draw the diagrams, its easier for me that way. Thanks for the help
6. The P is for >174

So it is after the mean as P(X<174) = 0.7
7. I didnt get it quite...Are we changing the sides because 0.3 isn't in the tables?
8. (Original post by Warfare)
I didnt get it quite...Are we changing the sides because 0.3 isn't in the tables?
no

we are not changing sides at all for the 174 ... it is more than the mean because we are given that P(x<174) = 70%
9. sorry all this time it was 172* not 174.Yeah but in the solution booklet i have, it says the 2 equations will be P(X<154) = 0.05, P(X>172) = 0.3.
Why could they write P(X>172) = 0.3 which is at the end of the diagram, past the mean. Isn't this supposed to be before the mean as its 30%. Under what conditions will i know when to shade which part in the diagram we are looking for whether it would be after or before the mean?
10. You're missing a crucial concept. The distribution is symmetrical. Probability is given by the area under the curve. There will always be two places where P(...) = 0.3 or any other probability apart from P(...) = 0.5, which will be in the middle of the curve and hence be the mean. When your given an X value you have to decide which side of the mean the probability area will lie. If it lies to the left of the mean you will always get a negative Z value when you standardise and a positive Z on the right.

Hope this helps.
11. (Original post by Warfare)
sorry all this time it was 172* not 174.Yeah but in the solution booklet i have, it says the 2 equations will be P(X<154) = 0.05, P(X>172) = 0.3.
Why could they write P(X>172) = 0.3 which is at the end of the diagram, past the mean. Isn't this supposed to be before the mean as its 30%. Under what conditions will i know when to shade which part in the diagram we are looking for whether it would be after or before the mean?
It is just common sense!

We know the area toward the right side of mean is 0.5, and toward the left is also 0.5.

So if they give us P(X>172) = 0.3, this means that our region lies in the right side of the mean. Just think about the equation and you will understand, if P(X>v)=0.6, then we will know that the point 'v' is in the left side of the graph.

I will suggest you watch videos at www.examsolutions.co.uk

Have you read the examples from the book?
They would be explaining well, you are just confusing a extremely simple concept.
12. Sorry guys, I got it. Yeah i was definately being stupid, haha. Thanks for the help, well appreciated!

Updated: May 12, 2012
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