Sampling - Central Limit Theorem
Sampling - Central Limit Theorem
The amount of rainfall \(X\) in a certain city per day has mean \(1.3\) metres and variance \(2.8\) square metres. The amount of rainfall for a sample of \(60\) days is collected.
- Calculate the mean and variance of \(\overline{X}\).
- Find the probability that the mean amount of rainfall exceeds \(0.8\) metres.
- State two assumptions about the sample used in obtaining this estimate in (ii).
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Answer:(i) \(E(\bar X)=1.3,\ \operatorname{Var}(\bar X)=\frac{7}{150}\) (ii) \(0.990\text{ (3 s.f.)}\) (iii) Randomly selected days, with independent rainfall amounts having the population mean and variance.
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