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Chapter 6: Q5 (page 261)

Notation

a. Identify the values of μ and σ for the standard normal distribution.

b. What do the symbols μx¯ and σx¯represent?

Short Answer

Expert verified
  1. The symbols μandσ represent the mean and standard deviation of population values respectively. Thus, μ=0,andσ=1for standard normal distribution.
  1. The symbols μx¯,σx¯represent the mean and standard deviation of all the sample mean values of a specific sample size respectively.

Step by step solution

01

Given information

Certain notations are mentioned.

02

Describe the random variable for population

a.

Let X be the random variable for population of all observations, which follows standard normal distribution.

The mean of the population is represented by μ. For standard normal distribution, mean is known to be 0.

The standard deviation of the population is represented by σ. For standard normal distribution, standard deviation is known to be 1.

Thus, X~Nμ=0,σ=1.

03

Describe the random variable for samples

b.

Let be the random variable for sample means of different equally sized samples taken from population.

The mean of the sample mean distribution is μx¯.

The standard deviation of sample mean distribution is σx¯.

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