Porisma

Worked solution

Use the standard normal model directly

The source labels this again as Example 4 (Self-directed Learning). For Z∼N(0,1)Z\sim N(0,1), find (i) P(0.32<Z≤1.3)P(0.32<Z\le 1.3) and (ii) a such that P(Z<a)=0.156P(Z<a)=0.156.

CJC · Lecture · Example 4

(i) Evaluate the interval

The standard normal has μ0 and σ1. Use normalcdf(0.32,1.3,0,1). The source calculator screen displays 0.2776836805, giving 0.278\boxed{0.278} (3 s.f.). Including the upper endpoint does not change a continuous probability.

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(ii) Find the left-tail quantile

Use invNorm(0.156,0,1,LEFT). The source screen displays −1.011034335, so a=−1.01\boxed{a=-1.01} (3 s.f.). The left area 0.156 is below 0.5, so the negative cutoff is consistent with the sketch of a standard normal curve.

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Common mistakes

This is a second printed Example 4, separate from the distinction-cutoff example on the preceding page. Its model is already standard normal, so use mean 0 and standard deviation 1.

Read the hint