Pure Mathematics
Statistics

Worked Example 4

The height of a species of plant has a normal distribution with mean [latex]34[/latex] cm and standard deviation of [latex]\sqrt{78}[/latex] cm. A random sample of [latex]13[/latex] plants is taken and the mean height is calculated. Find the probability that

(i)

The sample mean lies between [latex]29[/latex] cm and [latex]35[/latex] cm,

(ii)

[latex]P\left( {{X}{1}}+{{X}{2}}+…+{{X}_{13}}>450\text{cm} \right)[/latex]

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