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.

Question 1 out of 5.
Suppose you have a normal distribution with a mean of 6 and a standard deviation of 1. What is the probability of getting a Z score of exactly 1.2?

Question 2 out of 5.
You decide to use the normal distribution to approximate the binomial distribution. You want to know the probability of getting exactly 6 tails out of 10 flips. First you find the mean and SD of the normal distribution, and then you compute the area:

 at exactly 6

 from 5.5 to 6.5

 from 0 to 6

 from 6 to 10

Question 3 out of 5.
You decide to use the normal distribution to approximate the binomial distribution. You want to know the probability of getting from 7 to 13 heads out of 20 flips. You compute the area:

 from 7.5 to 13.5

 from 7.5 to 12.5

 from 7 to 13

 from 6.5 to 13

 from 6.5 to 13.5

Question 4 out of 5.
The normal approximation to the binomial is most accurate for which of the following probabilities?

 .2

 .5

 .8

Question 5 out of 5.
The normal approximation to the binomial is most accurate for which of the following sample sizes?

 4

 8

 12