Question 1127240: Assume that X is normally distributed with a mean µ = $64. Given that P(X ≥ $75) = 0.2981, we can calculate that the standard deviation of X is?
I'd like a detailed explanation, please.
Thank you in advance
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Assume that X is normally distributed with a mean µ = $64. Given that P(X ≥ $75) = 0.2981, we can calculate that the standard deviation of X is?
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If the right tail of X is 0.2981, the left tail is 0.7019
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Then z = invNorm(0.7019) = 0.5299
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Using x = z*s + u, solve for "s".
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75 = 0.5299*s + 64
0.5299s = 11
s = 20.76
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To better see what is happening with this problem,
sketch a normal curve, put 64 as the mean, shade
the right tail P(x>=75) = 0.2981.
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Cheers,
Stan H.
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