Math · Introductory statistics · Worked example
Find a probability between two values
Heights are normal with mean 170 cm and standard deviation 8 cm. What fraction lie between 160 cm and 180 cm?
Standardize both ends
Subtract the left areas
Φ(1.25) ≈ 0.8944 and Φ(−1.25) ≈ 0.1056.
Round honestly
With unrounded areas the difference is 0.78870, so about 0.789: 78.9% of heights lie in this range.
Result
About 0.789, or 78.9%.
Your turn
What fraction of a normal distribution lies within one standard deviation of its mean?
Show the answer and explanation
About 0.6827, or 68%.
Φ(1) − Φ(−1) ≈ 0.8413 − 0.1587.
Keep exploring
In Statistics, set the tail to two-sided at 1.25: P(|X| ≥ 1.25) ≈ 0.2113 is the part outside the range, and 1 − 0.2113 = 0.7887.
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