Maths: Applications and Interpretation · Statistics and probability. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
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Many measurements, such as heights, masses and times, follow a normal distribution. Its graph is a bell-shaped curve that is symmetrical about the mean μ, so the mean, median and mode are equal. The standard deviation σ controls how wide the bell is.
The area under the curve between two values is the probability that X lies between them. The total area is 1, with 0.5 on each side of the mean. Symmetry often gives an answer with no calculator.
For most questions use the calculator: normal cdf finds a probability from values, and inverse normal finds the value from a probability (an area to the left).
Students enter the area on the wrong side in inverse normal. The calculator expects the area to the left, so for "the highest 5%" enter 0.95, not 0.05. Also enter the standard deviation σ, not the variance σ2.
Answer: P(40 < X < 70) ≈ 0.815
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