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Prediction Intervals and Standard Scores

Please could anyone help explaining prediction intervals and standard scores? I literally can't get my head around how the values on the Wikipedia page are obtained compared to normal standard scores.

If we look at the Wikipedia page (and many other sources), the z-scores are listed as:

https://en.wikipedia.org/wiki/Prediction_interval

Prediction interval	z
50%	0.67
90%	1.64
95%	1.96
99%	2.58

However, the calculation to obtain the Z score on the Wikipedia page seems to require knowledge of the value of the future observation (X).

Say for example, that I wished to obtain the z-score for a 25% prediction level. Please could someone walk me through it?

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