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%.