Maths Statistics 1 Question Problem.

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Roha125
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[attach]8.050708050728051e+23[/attach] [attach]8.050708050728051e+23[/attach]
Can anyone explain me how 7.b) is solved.I am not understanding how 0.9426 is broken down to 0.9713 and .0287.
Paper Reference-2016 June S1 IAL
Last edited by Roha125; 2 years ago
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username3249896
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Sketch a normal curve, the midpoint of 1006 - w and w is the mean
the central area is 0.9426
due to symmetry, P(X < 1006-w) = 0.0287 and P(X > w) = 0.0287
https://imgur.com/a/k397rng

otherwise
z corresponding to 1006 - w = (503-w)/sigma
z corresponding to w = (w-503)/sigma
the probability is Φ[(w-503)/σ] - Φ[(503-w)/σ] = 2 Φ[(w-503)/σ] - 1
hence 2 Φ[(w-503)/σ] - 1 = 0.9426
so Φ[(w-503)/σ] is found
hence w is found
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