# Normal and Sampling Distributions - PowerPoint PPT Presentation

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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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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.