Worked solution
Practise standard-normal intervals and two tails
For , find (i) , (ii) and (iii) .
CJC · Lecture · Self-Practice 3
(i) An interval across zero
Use normalcdf(−2.56,0.134,0,1) to obtain approximately 0.5480651046, so the answer is (3 s.f.). The ≤ endpoint has no effect on this continuous probability.
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(ii) A right tail
Use normalcdf(1.863,10^99,0,1) to obtain approximately 0.0312311331, giving (3 s.f.).
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(iii) Outside a central interval
The printed prompt has absolute-value bars: means or . By symmetry,
Thus the answer is (3 s.f.). Equivalently subtract the interval probability between −0.754 and 0.754 from 1. The printed source gives the three short answers; the steps here explain them.
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Common mistakes
Retain the absolute-value bars in (iii): the question uses both tails. A single upper tail at 0.754 is about 0.225, which is only half the required probability.