CAIE S1 2013 June — Question 1 3 marks

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2013
SessionJune
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicNormal Distribution
TypeLinear relationship μ = kσ
DifficultyStandard +0.3 This is a straightforward normal distribution problem requiring standardization and inverse normal lookup. The linear relationship μ = 5σ reduces it to one unknown, and the calculation is routine once set up: (20-5σ)/σ = 1.45 from tables, giving σ = 4 and μ = 20. Slightly above average difficulty due to the algebraic setup with the constraint, but still a standard S1 exercise.
Spec2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation
1 The random variable \(Y\) is normally distributed with mean equal to five times the standard deviation. It is given that \(\mathrm { P } ( Y > 20 ) = 0.0732\). Find the mean.
Question 1:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(z = 1.452\)B1 Rounding to \(\pm 1.45\)
\(1.452 = \frac{20 - \mu}{\mu/5}\)B1 \(\frac{20-\mu}{\mu/5}\) or \(\frac{20-5\sigma}{\sigma}\) seen oe
\(\mu = 15.5\)B1 [3] Rounding to correct answer 
## Question 1:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $z = 1.452$ | B1 | Rounding to $\pm 1.45$ |
| $1.452 = \frac{20 - \mu}{\mu/5}$ | B1 | $\frac{20-\mu}{\mu/5}$ or $\frac{20-5\sigma}{\sigma}$ seen oe |
| $\mu = 15.5$ | B1 **[3]** | Rounding to correct answer |

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1 The random variable $Y$ is normally distributed with mean equal to five times the standard deviation. It is given that $\mathrm { P } ( Y > 20 ) = 0.0732$. Find the mean.

\hfill \mbox{\textit{CAIE S1 2013 Q1 [3]}}
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