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silverangel's avatar

How to solve this statistical problem?

Asked by silverangel (936points) May 1st, 2012

The question is:
The random variable X is normally distributed with mean 79 and variance 144.
It is known that P(79-a<= X <= 79 +b) = 0.6463. This information is shown in the image below:

Given that P(X>=79+b) = 2P(X<= 79-a)

Show that the area of the shaded region is 0.1179

Actually the answer includes ⅓(0.3537) = 0.1179
it’s just that I don’t know what the (⅓) is? or where did it come from? Can you please explain it?

Thanks in advance

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3 Answers

flutherother's avatar

The graph is in three sections, the left hand bit, the middle bit and the right hand bit. The middle bit is 0.6463 so the other two bits must total 1— 0.6463 = 0.3537.

The bit to the right is twice the size of the bit to the left (according to your equations) therefore the bit to the left is a third of 0.3537 and the bit to the right is two thirds of 0.3537. Simples!

Salem88's avatar

@flutherother – Oh, maybe you should try that equation again. You don’t want to flunk the class, do you? As soon as I have time to learn to “link” you to proper answer, we can trust each other’s calculations:-) weekend traffic is heavy.

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