5.5.2—Problems concerning a variable X

Use the normal CDF for P(X≤x), complements for upper tails and differences for intervals. Inverse normal questions solve for x from a stated probability.

Draw the tail or interval, standardise consistently and undo the transformation only after finding the z-value. Check whether the resulting value lies in the physical domain.

The central 90% interval for a normal variable uses z≈±1.645, so bounds are μ±1.645σ.

“At least” and “more than” are upper tails, while “between” requires subtracting two cumulative probabilities.