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Worked solution

Practise inverse-normal cutoffs

For X∼N(60,52)X\sim N(60,5^2), find

(i) mm given P(X<m)=0.2324P(X<m)=0.2324 and

(ii) nn given P(X>n)=0.837P(X>n)=0.837.

CJC · Lecture · Self-Practice 2

(i) Left-tail cutoff

Use μ60 and σ5 with invNorm(0.2324,60,5,LEFT). This gives approximately 56.34517065, so m=56.3\boxed{m=56.3} (3 s.f.). Since the given left area is below 0.5, the cutoff is below 60.

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(ii) Right-tail cutoff

Use invNorm(0.837,60,5,RIGHT). Equivalently the left area is 1−0.837=0.1631-0.837=0.163, so use invNorm(0.163,60,5). The cutoff is approximately 55.08898652, giving n=55.1\boxed{n=55.1} (3 s.f.).

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Common mistakes

The source provides short answers 56.3 and 55.1; the calculator routes here explain them. Do not input the variance 25 as σ, and do not use 0.837 as a LEFT area.

Read the hint