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Normal and Sampling Distributions

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Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, m, and variance, s2 The random variable Z = (X-m)/s is normal with mean 0 ... – PowerPoint PPT presentation

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Date added: 26 December 2018
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Title: Normal and Sampling Distributions


1
Normal and Sampling Distributions
  • A normal distribution is uniquely determined by
    its mean, m, and variance, s2
  • The random variable Z (X-m)/s is normal with
    mean 0 and variance 1
  • The normal probability density function is
    defined on page 227 and integrated in Table E.2
    on page 834

2
Sampling Distributions
  • A sampling distribution is the probability
    distribution of a random variable that is a
    sample statistic
  • Sample mean
  • Sample proportion
  • Sample standard deviation
  • Sample correlation coefficient

3
Central Limit Theorem
  • The sampling distribution of the sample mean is
    approximately normal
  • The larger the sample size, n, the more closely
    the sampling distribution of the sample mean will
    resemble a normal distribution.

4
The Sampling Distribution of the Sample Mean
  • Mean m, the same as the mean of X
  • Variance s2/n, the variance of X divided by
    sample size

5
The Sampling Distribution of the Sample Proportion
  • Mean p, the population proportion of or the
    probability of success in the binomial trial
  • Variance p(1-p)/n.
  • The binomial distribution is approximately normal
    if np and n(1-p) are both at least 5.
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