The sample mean and the central limit theorem Problem set A Answers

1. (a) \(\bar{X}\sim N(52,\,5)\)
2. (b) 2.24…

\(P(\bar X<145)\) = 0.159

1. (a) \(\bar{X}\approx N\left(28,\,\dfrac{49}{45}\right)\)
2. (b) It cannot be found.
3. (c) \(\bar{X}\sim N(28,\,2.45)\)

0.115

0.0173

0.254

1. (a) 0.345
2. (b) 0.0228
3. (c) A mean of several values varies much less than one value, so a mean far above the population mean is rarer.

1. (a) 0.383
2. (b) 0.683
3. (c) It increases. Larger samples give means closer to the population mean.