Chapter 6 - The Normal Distribution

correction for continuity

when using normal-curve areas to approximate the probability that an observed value of a binomial random variable will be between two whole numbers, inclusive, we subtract 0.5 from the smaller whole number and add 0.5 to the larger whole number before finding the area under the normal curve.

standardized normally distributed variable

subtracting a normally distributed variable its mean and then dividing by its standard deviation results in this. z = (x-u)/o

inverse cumulative probability

the observation whose cumulative probability is equal to the specified area

normal scores

the observations expected for a variable having the standard normal distribution

cumulative probability

The area under the associated normal curve of a normally distributed variable that lies to the left of a specified value; the probability that the variable will be less than or equal to the specified value

density curves

the shape of a distribution as a smooth curve. It is always on or above the horizontal axis, and the total area under the curve (and above the horizontal axis) equals 1.

parameters

we often identify a normal curve by stating the corresponding mean and standard deviation, which are called this

z(a)

This is used to denote the z-score that has an area of a (alpha) to its right under the standard normal curve

standard normal curve

a normally distributed variable having mean 0 and standard deviation 1 is said to have this curve

standard normal distribution

a normally distributed variable having mean 0 and standard deviation 1 is said to have this distribution

normal probability plot

a plot of the observed values of the variable

normally distributed population

if a variable of a population is normally distributed and is the only variable under consideration, it is this

normal curve

a special type of bell-shaped curve, with normal distribution

approximately normally distributed variable

a variable is shaped roughly like a normal curve

empirical rule

aka 68-95-99.7 rule. Approximately 68% of the observations lie within 1 standard deviation of the mean. 95% lie within 2 standard deviations, and 99.7% lie within 3 standard deviations.

z-curve

aka standard normal curve

normally distributed variable

aka normal distribution. a variable is said to be this if its distribution has the shape of a normal curve

normal distribution

aka normally distributed variable. a variable is said to have this if its distribution has the shape of a normal curve

68-95-99.7 rule

aka the Empirical Rule. Approximately 68% of the observations lie within 1 standard deviation of the mean. 95% lie within 2 standard deviations, and 99.7% lie within 3 standard deviations.