Chapter 6.pdf

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Biology (Biological Sciences)
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Blaine Mullins

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Chapter 6: Normal Distributions Since normal distributions play a large role in statistics, we will talk mainly about normal distributions in this chapter. The normal distributions are symmetric, single peaked, bell-shaped density curves. All normal distributions have the same overall shape. The exact density curve for a particular normal distribution is described by giving its mean  and its standard deviatin . The mean is located at the center of the symmetric curve and is the same as median. Changing  without changing  moves the normal curve to a new location without altering its spread. The standard deviation controls the spread of a normal curve. Example 6.1: If the random variable Z has the standard normal distribution, find () 7 5P.(Z1  () 7 5P.(Z1  Top-Hat Question (Review 6-1): (c) P(1.43  Z 1.37) Example 6.2: If the random variable Z has the standard normal distribution, locate the value of z that satisfies (a) P(Z z )  0.1736 (b) P(Z  z)  0.025 Top-Hat Question (Review 6-2): (c) P(z  Z  z)  0.90 Y YMean  The standardized variable Z   has mean 0 and Standard deviation  standard deviation 1. It does not depend on the unit of measurement. IfY has a normal distribution with mean of  and standard deviation of  , then Z has the standard normal distribution. Example 6.3: If the random variable Y has a normal distribution of  60 and standard deviation of  4 , finP(55  63). Example 6.4: Replacement times for CD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.4 years. Find the
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