The heights, $$\(h\)$$ centimetres, of a random sample of 100 fully grown animals of a certain species were measured. The results are summarised below. $$\( n=100 \quad \Sigma h=7570 \quad \Sigma h^{2}=588050 \)$$ Four random samples were taken and a $$\(99 \%\)$$ confidence interval for the population mean, $$\(\mu\)$$, was found from each sample. Find the probability that all four of these confidence intervals contain the true value of $$\(\mu\)$$. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

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