In a normal distribution where X ~N(0,1) , approximately what is the probability that X is between -1 and 0.

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BlackTom AI · Accepted Answer

This question asks for the probability that a standard normal variable X ~ N(0,1) falls between -1 and 0.

First, note that the standard normal distribution is symmetric about 0, with CDF denoted by Phi. The probability that X is between a and b is Phi(b) - Phi(a).

In our case, a = -1 and b = 0. So the probability is Phi(0) - Phi(-1).

We know Phi(0) = 0.5 because the median of a symmetric distribution around 0 is 0. 
Phi(-1) equals 1 - Phi(1) due to symmetry: Phi(-z) = 1 - Phi(z). The value Phi(1) is approximately 0.8413, hence Phi(-1) ≈ 1 - 0.8413 = 0.1587.

Therefore, the probability is 0.5 - 0.1587 ≈ 0.3413, which is about 34.13%.

Note on the given data: the options field is empty in this item, so there is no list of choices to evaluate. If a multiple-choice list were provided, we would map this numeric result to the closest option and explain any rounding differences. The key takeaway is that P(-1 ≤ X ≤ 0) ≈ 0.3413, i.e., about 34% of the distribution lies in that interval.

ERMCPS5350_003_2025_3 - INTRO TO QUANTITATIVE RISK MANAGEMENT 6. Quiz for Class 6

In a normal distribution where X ~N(0,1) , approximately what is the probability that X is between -1 and 0.

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