# The Standard Normal Distribution - Page 6

Questions

- What is the mathematical difference between the probability density functions of a normal distribution and a standard normal distribution?
- What is the mathematical formula for the probability density function of the general normal distribution?
- Do all random distributions follow a "normal" distribution?
- What is the standard deviation of the standard normal distribution?
- What is the Gaussian function?
- What determines if data will follow a normal distribution?
- What is the Gaussian function?
- Is the sum of two Gaussian functions still a Gaussian function? What implication does this have for adding data sets?
- Which probability distributions are considered "bell-shaped?"
- Why does the standard normal distribution have a kurtosis of 0?
- What is the characteristic function of a normal distribution?
- What is the moment generating function of a Gaussian distribution?
- Suppose that the fish in my pond have mean length 20 inches with a standard deviation of 4 inches. What is the probability that in an independent random sample, the total length of 5 fish caught from this pond will be between 95 and 110 inches in length?
- How do you determine the percentage of eruptions that last between 92 and 116 seconds with a mean of 104 and a standard deviation of 6?
- The mean value of a land and building per acre from a sample of a farm is $1500, with a standard deviation of $200. What is the percent of farms whose land and building values acre are between $1300 and $1700?
- The heights of women at a large university are approximately bell-shaped, with a mean of 64 inches and standard deviation of 2 inches. What is the probability that a randomly selected woman from this university is 66 inches or taller?
- For a normal distribution, what is the percentage of data that is between #mu - 0.5 sigma# and #mu + 0.5 sigma#?
- There is a normal distribution with min = 4, max = 16 and mean = 10. What is the standard deviation?
- How does central tendency relate to normal distribution?
- What is the 90th percentile of a standard normal distribution?