Summary-L05

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  • A normal density curve is symmetric and bell-shaped. The curve lies above the horizontal axis and the total area under the curve is equal to 1.
  • A standard normal distribution has a mean of 0 and a standard deviation of 1. The 68-95-99.7% rule states that when data are normally distributed, approximately 68% of the data lie within 1 standard deviation from the mean, approximately 95% of the data lie within 2 standard deviations from the mean, and approximately 99.7% of the data lie within 3 standard deviations from the mean.
  • A z-score tells us how many standard deviations away from the mean a given value is. It is calculated as: $\displaystyle{z = \frac{\text{value}-\text{mean}}{\text{standard deviation}} = \frac{x-\mu}{\sigma}}$
  • The probability applet allows us to use z-scores to calculate proportions, probabilities, and percentiles.
  • A Q-Q plot is used to assess whether or not a set of data is normally distributed.