| Exam Board | Edexcel |
|---|---|
| Module | S3 (Statistics 3) |
| Year | 2020 |
| Session | October |
| Marks | 16 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Linear combinations of normal random variables |
| Type | Mixed sum threshold probability |
| Difficulty | Standard +0.3 This is a standard S3 question on linear combinations of normal random variables. Parts (a) and (b) are routine applications of the sum of normals formula requiring only calculation of means and variances. Part (c) requires algebraic manipulation to find n from a probability equation, but follows a predictable pattern for this topic. The question is slightly easier than average as it involves straightforward application of well-practiced techniques without requiring novel insight or complex problem-solving. |
| Spec | 5.04b Linear combinations: of normal distributions |
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| Q7 | |
7. A company makes cricket balls and tennis balls.
The weights of cricket balls, $C$ grams, follow a normal distribution
$$C \sim \mathrm {~N} \left( 160,1.25 ^ { 2 } \right)$$
Three cricket balls are selected at random.
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\item Find the probability that their total weight is more than 475.8 grams.
The weights of tennis balls, $T$ grams, follow a normal distribution
$$T \sim \mathrm {~N} \left( 60,2 ^ { 2 } \right)$$
Five tennis balls and two cricket balls are selected at random.
\item Find the probability that the total weight of the five tennis balls and the two cricket balls is more than 625 grams.
A random sample of $n$ tennis balls $T _ { 1 } , T _ { 2 } , \ldots , T _ { n }$ is taken.\\
The random variable $Y = ( n - 1 ) T _ { 1 } - \sum _ { r = 2 } ^ { n } T _ { r }$\\
Given that $\mathrm { P } ( Y > 40 ) = 0.0838$ correct to 4 decimal places,
\item find $n$.\\
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\hfill \mbox{\textit{Edexcel S3 2020 Q7 [16]}}