| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2024 |
| Session | September |
| Marks | 4 |
| Topic | Normal Distribution |
| Type | Find mean from probability statement |
| Difficulty | Moderate -0.3 This is a straightforward inverse normal distribution problem requiring a single step: look up the z-score for probability 0.242, then solve μ = 22 - 5z. It's slightly easier than average because it only requires one calculation with no conceptual complexity, though students must correctly handle the left-tail probability. |
| Spec | 2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation |
4.
The random variable $H$ has the distribution $\mathrm { N } \left( \mu , 5 ^ { 2 } \right)$. It is given that $\mathrm { P } ( H < 22 ) = 0.242$. Find the value of $\mu$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Statistics 2024 Q4 [4]}}