CAIE S2 2016 June — Question 1 4 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2016
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCentral limit theorem
TypeCalculate probabilities using sample mean distribution
DifficultyModerate -0.5 This is a straightforward application of the Central Limit Theorem requiring only standardization and normal table lookup. The question directly provides all necessary parameters (μ, σ, n) and asks for a single probability calculation with no complications or multi-step reasoning, making it slightly easier than average.
Spec5.05a Sample mean distribution: central limit theorem
1 The length of time, in minutes, taken by people to complete a task has mean 53.0 and standard deviation 6.2. Find the probability that the mean time taken to complete the task by a random sample of 50 people is more than 51 minutes.
Question 1:
AnswerMarks Guidance
Answer/WorkingMark Guidance
\(\frac{6.2}{\sqrt{50}}\) or \(\frac{6.2^2}{50}\)B1 seen or implied
\(\frac{51-53}{6.2\div\sqrt{50}}\) \((= -2.281)\)M1 allow without \(\div\sqrt{50}\)
\(P(z > -2.281) = \phi(2.281)\)M1 for finding correct area consistent with working
\(= 0.989\) (3 sf)A1 [4] as final answer 
## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $\frac{6.2}{\sqrt{50}}$ or $\frac{6.2^2}{50}$ | B1 | seen or implied |
| $\frac{51-53}{6.2\div\sqrt{50}}$ $(= -2.281)$ | M1 | allow without $\div\sqrt{50}$ |
| $P(z > -2.281) = \phi(2.281)$ | M1 | for finding correct area consistent with working |
| $= 0.989$ (3 sf) | A1 [4] | as final answer |
1 The length of time, in minutes, taken by people to complete a task has mean 53.0 and standard deviation 6.2. Find the probability that the mean time taken to complete the task by a random sample of 50 people is more than 51 minutes.

\hfill \mbox{\textit{CAIE S2 2016 Q1 [4]}}
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