Edexcel S3 — Question 4 7 marks

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicLinear combinations of normal random variables
TypeMixed sum threshold probability
DifficultyStandard +0.8 This S3 question requires understanding of sums of independent normal distributions, calculating combined mean and variance for multiple random variables (8 large + 3 small bags), then finding a probability using standardization. While the concepts are standard for S3, the multi-step calculation with two different distributions and careful arithmetic makes it moderately challenging, above average difficulty but not requiring novel insight.
Spec5.04b Linear combinations: of normal distributions
The mass of waste in filled large dustbin bags is normally distributed with a mean of 6.8 kg and a standard deviation of 1.5 kg. The mass of waste in filled small dustbin bags is normally distributed with a mean of 3.2 kg and a standard deviation of 0.6 kg. One week there are 8 large and 3 small dustbin bags left for collection outside a block of flats. Find the probability that this waste has a total mass of more than 70 kg. [7 marks]
Let \(T\) = total mass of waste
AnswerMarks Guidance
\(\therefore T \sim N(8(6.8) + 3(3.2), 8(1.5^2) + 3(0.6^2)) = \sim N(64, 19.08)\)M2 A2
\(P(T > 70) = P(Z > \frac{70-64}{\sqrt{19.08}})\)M1
\(= P(Z > 1.37) = 1 − 0.9147 = 0.0853\)M1 A1 (7) 
Let $T$ = total mass of waste
$\therefore T \sim N(8(6.8) + 3(3.2), 8(1.5^2) + 3(0.6^2)) = \sim N(64, 19.08)$ | M2 A2 |
$P(T > 70) = P(Z > \frac{70-64}{\sqrt{19.08}})$ | M1 |
$= P(Z > 1.37) = 1 − 0.9147 = 0.0853$ | M1 A1 | (7)
The mass of waste in filled large dustbin bags is normally distributed with a mean of 6.8 kg and a standard deviation of 1.5 kg. The mass of waste in filled small dustbin bags is normally distributed with a mean of 3.2 kg and a standard deviation of 0.6 kg.

One week there are 8 large and 3 small dustbin bags left for collection outside a block of flats. Find the probability that this waste has a total mass of more than 70 kg. [7 marks]

\hfill \mbox{\textit{Edexcel S3  Q4 [7]}}
This paper (8 questions)
View full paper
Q1 5 Q2 6 Q3 7 Q4 7 Q5 8 Q6 11 Q7 11 Q8 20