A manufacturer of candles claimed that it produced birthday candles with a mean burning time of \(6\

Question

A manufacturer of candles claimed that it produced birthday candles with a mean burning time of $6$ minutes. A random sample of $150$ birthday candles was tested and the burning times, $X$ minutes, were summarized by $\sum{(x-5)=120}$ and $\sum{{{(x-5)}^{2}}=638}$ . Calculate the unbiased estimates for the mean $\mu $ and variance${{\sigma }^{2}}$ .

Accepted Answer

$\hat\mu=5.8,\quad \widehat{\sigma^2}=\frac{542}{149}\approx3.64$

2005 SAJC P2 Q28

2005 SAJC P2 Q28

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