In the last years special "ovals" appear increasingly often in diagrams and applets for discussing crucial items of statistical inference (when dealing with confidence intervals for an unknown probability p; approximation of the binomial distribution by the normal distribution; especially in German literature, see e.g. [Meyer, "Stochastik in der Schule" 2011; 31:18-22] or [Riemer, 'Statistik unterrichten." "Eine handlungsorientierte Didaktik der Stochastik;" 2023, p. 69ff]). These applets concerning confidence intervals aim at illustrating vividly the crucial differences (as we know, often vague for students) and connections between confidence intervals and prediction intervals. In English literature such applets seem to be not so well known, thus at the beginning, we describe how they work and highlight their high potential for teaching and learning. The fact that the mentioned ovals are, actually, ellipses is not important for stochastic purposes which is probably the reason why one can hardly find related explanations in the literature. Another aim of this paper is to explain the ellipse shape in a preferably elementary manner involving geometry, even spatial geometry.