Worked solution
Practise interval, left-tail and central probabilities
For , find
(i) ,
(ii) and
(iii) .
CJC · Lecture · Self-Practice 1
(i) An interval
Use mean 2 and standard deviation : normalcdf(1.8,2.9,2,√3) gives 0.2442978362, so the answer is (3 s.f.).
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(ii) A left tail
Use normalcdf(−10^99,2.8,2,√3) to obtain 0.6779163887, so (3 s.f.).
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(iii) Within two standard deviations
Convert into . Use normalcdf(2−2√3,2+2√3,2,√3) to obtain 0.9544997361, giving (3 s.f.). This agrees with the approximately 95.4% rule for two standard deviations.
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Common mistakes
The second parameter 3 is the variance. In (iii), the half-width 2√3 is twice the standard deviation, not twice the variance. The printed source provides short answers; these conversions and calculator steps explain them.