SOLUTION: Please help me understand ... If represents a random variable coming from a normal distribution and P(X<5)=0.47, then P(X>5)=0.53. True or False. Step by step please, thank you so

Question 1199995: Please help me understand ... If represents a random variable coming from a normal distribution and P(X<5)=0.47, then P(X>5)=0.53. True or False. Step by step please, thank you so much.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the normal distribution curve has a total area under it of 1.
if p(x < 5) = .47, then p(x > 5) = 1 - .47 = .53.
that is true.
at any point along the normal distribution curve, the area below the point is equal to 1 minus the area above the point since the total area is always equal to 1.
here's an example.
z-score is 1.5
area above the mean = .0668
area below the mean = .9332
area above the mean plus area below the mean = 1

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