Mixed practice: normal combinations, sample means and the central limit theorem Problem set A Answers

1. (a) \(W\sim N(131,\,299)\)
2. (b) \(W\sim N(0,\,22)\)
3. (c) \(W\sim N(63,\,18)\)

1. (a) \(\bar{X}\sim N(75,\,3)\)
2. (b) Mean 2.4, variance 0.025

1. (a) \(\bar{X}\approx N(45,\,1.35)\)
2. (b) It cannot be found.
3. (c) \(\sum X_i\approx N(1800,\,3240)\)

0.0548

1. (a) \(T\sim N(19.7,\,5.36)\)
2. (b) 0.160

1. (a) Mean −0.7, standard deviation 1.42…
2. (b) 0.689
3. (c) 0.180

1. (a) 0.726
2. (b) 0.428

0.0829

0.873

0.303

0.186

1. (a) Mean 250, variance 0.5
2. (b) 0.0897

0.0249