Normal Distribution, Confidence Intervals for the Mean ...

Continuous Probabilities: Normal distribution , Confidence Intervals for the Mean, and Sample Size The Normal distribution Normal (Gaussian) distribution : a symmetric distribution , shaped like a bell, that is completely described by its mean and standard deviation. Mean or x Tail Standard Deviation or sd Every distribution has 2 tails. There are an infinite number of Normal curves. To be useful, the Normal curve is standardized to a mean of 0 and a standard deviation of 1. This is called a standard Normal curve. To use the standard Normal curve, data must first be converted to z-scores. Z-score: a transformation that expresses data in terms of standard deviations from the mean.. =.. For example: We have a sample that has a mean of 8 and a standard deviation of What is the z-score of an observation from this data set that has a value of 13?

For smallish sample sizes we use the t distribution. T distribution: a symmetric distribution, more peaked than the normal distribution, that is completely described by its mean and standard deviation for . k degrees of freedom or df (we will discuss this term in more detail later). The . df. for confidence intervals is . n-1. So for our ...

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  Distribution, Confidence, Interval, T distribution, Confidence intervals

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