Normal distribution

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5 Terms

1
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What is a normal distribution graph?

  • Has parameters µ, the population mean and σ², the population variance

  • is symmetrical (mean = median = mode)

  • Total area = 1

  • Point of inflection at µ + σ and µ - σ

<ul><li><p>Has parameters <span>µ, the population mean and σ², the population variance</span></p></li><li><p><span>is symmetrical (mean = median = mode)</span></p></li><li><p><span>Total area = 1</span></p></li><li><p><span>Point of inflection at </span>µ + σ and µ - σ</p></li></ul><p></p>
2
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Key percentages needed to know about normal distribution:

  • 68% of data lies within one standard deviation from mean

  • 95% of data lies within two standard deviations from the mean

  • 99.7% of data lies within three standard deviations from the mean

3
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The standardised normal distribution => Z

  • Useful for working out mean and standard deviation

<ul><li><p>Useful for working out mean and standard deviation</p></li></ul><p></p>
4
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Approximating binomial distribution

  • When N is large and P is close to 0.5 in binomial distribution, this can be used to work out mean and standard deviation.

<ul><li><p>When N is large and P is close to 0.5 in binomial distribution, this can be used to work out mean and standard deviation.</p></li></ul><p></p>
5
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Hypothesis testing with normal distribution:

  • All the other steps for hypothesis testing is same

  • IN THE PICTURE: the formulae present

<ul><li><p>All the other steps for hypothesis testing is same</p></li><li><p>IN THE PICTURE: the formulae present</p></li></ul><p></p>

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