Question 1182516: If X represents a random variable coming from a normal distribution and P (X < 10.7) =0.6, then P (X > 10.7) =0.4.
True
False Found 3 solutions by Theo, greenestamps, math_tutor2020:Answer by Theo(13342) (Show Source):
the reason is that the normal distribution curve is symmetric about the mean.
the area to the left of a score is equal to 1 minus the area to the right of the score.
this can be seen in the following graphs of the normal distribution curve.
in these graphs, i created a mean and a standard deviation that would give me the results of 10.7 having an area to the left of it of .6.
the area to the right of it became .4, which is equal to 1 minus .6.
The fact that the distribution is normal is irrelevant to the problem; showing the statement is true is trivial.
With a random variable, we consider the probability that the variable have a specific value to be 0. So in ANY probability distribution, the probability that x is greater than 10.7 is 1 minus the probability that x is less than 10.7.
Explanation: The two probabilities are complements, meaning that they add to 1.
So 0.6+0.4 = 1
The fact that P(A)+P(B) = 1 is being used here has nothing to do with the underlying probability distribution. So the "normal distribution" seems like a red herring in my opinion (ie it may be "clue" that's added intentionally to distract/mislead the reader).
Either x is less than 10.7, or it is larger than 10.7
We consider the case x = 10.7 itself to happen with probability 0 since throwing a dart to land *exactly* at this location is pretty much 0 chance of it happening. There's always going to be some slight error involved.
I guess to be more thorough, we could say and
Or we could say and to ensure that 10.7 itself is involved somehow. Though this is a trivial nitpicky detail.
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