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

1. (a) \(W\sim N(228,\,271)\)
2. (b) \(W\sim N(0,\,14)\)
3. (c) \(W\sim N(135,\,39)\)

1. (a) \(\bar{X}\sim N(120,\,6)\)
2. (b) Mean 8.5, variance 0.096

1. (a) \(\bar{X}\approx N\left(70,\,\dfrac{256}{36}\right)\)
2. (b) It cannot be found.
3. (c) \(\sum X_i\approx N(3500,\,12800)\)

0.202

1. (a) \(T\sim N(78.7,\,11)\)
2. (b) 0.0287

1. (a) Mean 0.5, standard deviation 1
2. (b) 0.309
3. (c) 0.159

1. (a) 0.609
2. (b) 0.311

0.179

0.884

0.779

0.214

1. (a) Mean 1000, variance 5
2. (b) 0.0495

0.00234