29650 Engineering Mathematics 2 - Tutorial sheet 3
Question 1
A 4 sided tetrahedral dice is weighted at one corner so that P (1) = P (2) = P (3) = 0.3 and P (4) = 0.1. The values of a random variable r are determined by a throw of this dice. Calculate:
1. The expected value E(r) of r
2. The variance V (r) of r
3. The minimum number of times N that the dice must be throw to be 95% confident that the sample mean is within ±0.1 of the true mean E(r)
Question 2
A 6-sided dice is weighted such that P (1) = P (2) = P (3) = P (4) = 1− p/4 and P (5) = P (6) = p/2, (0 ≤ p ≤ 1)
. Let r be the random variable whoes value is determined by a throw of this dice. Calculate:
1. The expected value E(r) as a function of p
2. The variance V (r) as a function of p
3. The minimum number of times N that the dice must be throw to be 95% confident that the sample mean is within ±0.2 of the true mean E(r), as a function of p
4. The value of p for which N is maximum
Question 3
A chocolate factory produces 100g bars of chocolate. The weight of a chocolate bar is modelled as a random variable r. Quality control dictates that the average weight of a chocolate bar is 100g with a variance of 0.2g2 . Each morning 10 chocolate bars are weighed. This morning their weights were 100g, 102g, 100.5g, 98g, 101g, 99.5g, 98g, 100g, 97g, 101g. Based on this sample, should the factory manager conclude that the factory has failed its quality control test (p = 0.05)?