In your question, you state that $P(z\geq 3.9)= 0.000048$-this is that very small area ABOVE the $z$ score.Ĭonsider the following picture, the $P(z3.16)$ should be, but could not shade it in because, well, it is quite small!īut how are $z$-scores calculated? As stated, it is the area below the Normal distribution's curve. ![]() There does exist a very small amount of area (again, synonymous with probability) above $3.16\sigma$. The probability is the area below the Normal distribution's curve.įor a score of $z=3.16$, the area under the Normal distribution from $-\infty \sigma$ to $3.16\sigma$ is $\approx 1$ (this is the probability). You said anything $>z=3.16$ will have a probability = 1. Recall that a $z$-score is simply the number of standard deviations away from the mean ($\mu$).
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