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A normal variable has a mean μ and a standard deviation σ. What is the probability that the value of the variable is greater than μ − σ?

a. 80.1%
b. 74.1%
c. 90.2%
d. 84.1

User Harts
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1 Answer

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Final answer:

The probability that a value of a normal variable is greater than μ − σ is approximately 84.1%, due to the properties of the normal distribution where 68% of values lie within one standard deviation of the mean.

Step-by-step explanation:

The question you've asked is related to the properties of the normal distribution. In a normal distribution, the mean (μ) is the center of the distribution and the standard deviation (σ) is a measure of the spread of the distribution. The question asks about the probability that the value of the variable is greater than μ − σ.

In a standard normal distribution, approximately 68% of the values lie within one standard deviation of the mean (meaning between μ − σ and μ + σ). T

herefore, the area to the right of μ − σ, which is what you're looking for, would cover half of the 68% plus the 50% that lies beyond μ.

So we have 34% (half of 68%) + 50% = 84%.

Hence, the correct answer is d. 84.1%.

User Art Doler
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