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.