More on Normal Distributions

First, this section talks about the history of the normal distribution and the central limit theorem and the relation of normal distributions to errors. Then, it discusses how to compute the area under the normal curve. It then moves on to the normal distribution, the area under the standard normal curve, and how to translate from non-standard normal to standard normal. Finally, it addresses how to compute (cumulative) binomial probabilities using normal approximations.


  1. Because the normal distribution is continuous, the probability of any one specific point is 0.

  2. Because the normal distribution is continuous, the probability of any one specific point is 0. The solution is to round off and consider any value from 5.5 to 6.5 to represent an outcome of 6 tails. Using this approach, we figure out the area under a normal curve from 5.5 to 6.5.

  3. In order to include 7 flips, you need to start a little below it (6.5), and to include 13 flips, you need to go a little past it (13.5). So, you calculate the area from 6.5 to 13.5.

  4. It is most accurate for p=.5 because that makes the binomial distribution symmetric and closer to a normal distribution.

  5. The binomial distribution approaches a normal distribution as the sample size increases. Therefore the approximation is best when the sample size is highest.