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How do you find the probability of something greater than?
If you want a “greater-than” probability — that is, p(X > b) — take one minus the result from Step 4. If you need a “between-two-values” probability — that is, p(a < X < b) — do Steps 1–4 for b (the larger of the two values) and again for a (the smaller of the two values), and subtract the results.
Which is true about the standard normal distribution?
The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. The standard normal distribution is centered at zero and the degree to which a given measurement deviates from the mean is given by the standard deviation.
How to calculate the probability of one random variable being greater than another?
As you have pointed out in your question, to compute this probability, you need to find the distribution of D = X − Y.
Is the normal probability distribution a family of distributions?
The normal probability distribution, one of the fundamental continuous distributions of statistics, is actually a family of distributions (an infinite number of distributions with differing means (μ) and standard deviations (σ).
Why is the normal distribution a continuous distribution?
Because the normal distribution is a continuous distribution, we can not calculate exact probability for an outcome, but instead we calculate a probability for a range of outcomes (for example the probability that a random variable X is greater than 10). The normal distribution is symmetric and centered on the mean (same as the median and mode).
What is the probability of Z falling between 1 and 1?
Because the normal distribution is symmetric, we therefore know that the probability that z is greater than one also equals 0.1587 [p (z)>1 = 0.1587]. To calculate the probability that z falls between 1 and -1, we take 1 – 2 (0.1587) = 0.6826. The green area in the figure above roughly equals 68% of the area under the curve.