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# Stats Chapter 6

### Normal Probability Distributions

TermDefinition
Normal probability distribution Distribution of probabilities that plots all of its values in a symmetrical fashion and most of the results are situated around a probability's mean; values are equally likely to plot above or below the mean
What types of variables have a normal or an approximately normal distribution? Continuous random variables (weight) and Discrete random variables (score from test with set number of questions)
What are the first 2 properties of the standard normal distribution? 1) The total area under the normal curve is equal to 1. 2) The distribution is mounded and symmetrical; it extends indefinitely in both directions, approaching but never touching the horizontal axis
What are the other 3 properties of the standard normal distribution? 3) The distribution has a mean of 0 and a standard deviation of 1 4) The mean divides the area in half (0.50 on each side) 5) Nearly all the area is between z - -3.00 and 3.00
Standard normal distribution The normal distribution of the standard variable z
The standard normal distribution is also known as... Standard score Z-score
Binomial distribution Probability distribution of the discrete random variable x, the number of successes observed in "n" repeated trials; as "n" trials becomes larger, the probability distribution appears more normal
What is the main difference between the binomial and normal probability distribution? Binomial: random variable is discrete Normal: random variable is continuous
Continuity Correction Factor Addition and subtraction of 0.5 to the x-value to convert a discrete random variable into a continuous one
Mean in a binomial distribution u = np
Standard deviation in a binomial distribution o = sqrt(npq)
Rule for binomial distribution normal distribution provides a reasonable approximation to a binomial probability whenever the values of np and n(1-p) both equal or exceed 5.