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Rudiy27
3 years ago
7

X is normally distributed with mean 250 and standard deviation 40. what value of x does only the top 15% exceed?

Mathematics
1 answer:
lubasha [3.4K]3 years ago
3 0
The top 15% (85th percentile) is the cutoff value x such that

\mathbb P(X\le x)=\mathbb P\left(\dfrac{X-250}{40}\le\dfrac{x-250}{40}\right)=\mathbb P(Z\le z)=0.85

where z is the corresponding cutoff for the standardized normal distribution. We have z\approx1.0364, and so

\dfrac{x-250}{40}=z\implies x\approx291.456
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