EEB225H1 Lecture 10: T-Distribution

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The normal distribution is very common in nature. The normal distribution is fully described by its mean and standard deviation. Within a normal distribution, the mean, median and mode are the same. A normal distribution is symmetric around its mean. About 2/3 (68%) of random draws from a normal distribution are within one standard deviation of the mean. About 95% of random draws from a normal distribution are within two standard deviations (1. 96 sd) of the mean. Mean is zero: = 0. Standard deviation is one: = 1. Gives the probability of getting a random draw from a standard normal distribution greater than a given value. Standard normal is symmetric, so: pr[z > x] = pr[z < -x, pr[z < x] = 1 pr[z > x] All normal distributions are shaped alike, just with different means and variances. Any normal distribution can be converted to a standard normal distribution by: Z is called the standard normal deviate .

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