CAIE S2 2020 June — Question 1 4 marks

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2020
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear combinations of normal random variables
TypeSingle sum threshold probability
DifficultyStandard +0.3 This is a straightforward application of linear combinations of normal random variables. Students need to recognize that the sum of 6 independent N(40.4, 5.2²) variables follows N(6×40.4, 6×5.2²), then calculate P(Sum < 220) using standardization. It's a direct textbook exercise requiring only routine application of formulas with no problem-solving insight needed, making it slightly easier than average.
Spec5.04b Linear combinations: of normal distributions

1 The masses, in grams, of plums of a certain type have the distribution \(\mathrm { N } \left( 40.4,5.2 ^ { 2 } \right)\). The plums are packed in bags, with each bag containing 6 randomly chosen plums. If the total weight of the plums in a bag is less than 220 g the bag is rejected. Find the percentage of bags that are rejected.

Question 1:
AnswerMarks Guidance
AnswerMark Guidance
\(N(242.4, 162.24)\)B1
\(\frac{220 - 242.4}{\sqrt{162.24}} = -1.759\)M1
\(\phi(-1.759) = 1 - \phi(1.759) = 0.0393\)M1
\(3.93\%\)A1
Total: 4
## Question 1:

| Answer | Mark | Guidance |
|--------|------|----------|
| $N(242.4, 162.24)$ | B1 | |
| $\frac{220 - 242.4}{\sqrt{162.24}} = -1.759$ | M1 | |
| $\phi(-1.759) = 1 - \phi(1.759) = 0.0393$ | M1 | |
| $3.93\%$ | A1 | |
| **Total: 4** | | |

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1 The masses, in grams, of plums of a certain type have the distribution $\mathrm { N } \left( 40.4,5.2 ^ { 2 } \right)$. The plums are packed in bags, with each bag containing 6 randomly chosen plums. If the total weight of the plums in a bag is less than 220 g the bag is rejected.

Find the percentage of bags that are rejected.\\

\hfill \mbox{\textit{CAIE S2 2020 Q1 [4]}}