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The delivery time (in minutes) of a courier service is a random variable \(X\) with expectation \(\mu=30\) and variance \(V=25\). We take a random sample of \(n=64\) deliveries and denote their average delivery time by \(\overline{X}_{64}\).
Calculate the variance of the sample mean \(V(\overline{X}_{64})\).
Use the concentration inequality to bound the probability \(P(|\overline{X}_{64}-30|\ge 1.5)\).
Bound the probability that the mean delivery time is outside the interval \([28,32]\).
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