Lecture_13,_Chap_8,_Sec_1b_&amp;_2

# Lecture_13,_Chap_8,_Sec_1b_&_2 - Distribution of the...

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Distribution of the Sample Mean Learning objectives Understand the concept of a sampling distribution Describe the distribution of the sample mean for samples obtained from normal populations Describe the distribution of the sample mean for samples obtained from a population that is not normal 1 2 3

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Distribution of the Sample Mean This is great if our random variable X has a normal distribution However … what if X does not have a normal distribution What can we do? Wouldn’t it be very nice if the sampling distribution for X also was normal? This is almost true …
Distribution of the Sample Mean The Central Limit Theorem states: Regardless of the shape of the distribution, the sampling distribution becomes approximately normal as the sample size n increases Thus If the random variable X is normally distributed, then the sampling distribution is normally distributed for any sample size For all other random variables X , the sampling distributions are approximately normally distributed if n is 30 or higher Helpful Hint: Study Example 5 on pp.426-427 of your textbook.

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Distribution of the Sample Mean Example The most famous geyser in the world, Old Faithful in Yellowstone Nat’l Park, has a mean time between eruptions of 85 minutes and a standard deviation of 21.25 minutes. The distribution of time interval between eruptions is not normal. 1. What is the probability that a randomly selected time interval will be less than 75 minutes? 2. What is the probability that a random sample of 20 time intervals will have a mean less than 75 minutes? 3. What is the probability that a random sample of 30 time intervals will have a mean less than 75 minutes? 4. What is the probability that a random sample of 30 time intervals will have a mean longer than 100 minutes?
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## This note was uploaded on 08/04/2008 for the course STAT 250 taught by Professor Sims during the Spring '08 term at George Mason.

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Lecture_13,_Chap_8,_Sec_1b_&_2 - Distribution of the...

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