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Advanced Math Topics

Advanced Math Topics. 8.6/8.7 The Central Limit Theorem. The Central Limit Theorem. If large random samples of size y (the book uses n) when x > 30 are taken from a population with mean μ and standard deviation σ , and if a sample mean x is computed for each sample, then….

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Advanced Math Topics

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  1. Advanced Math Topics 8.6/8.7 The Central Limit Theorem

  2. The Central Limit Theorem If large random samples of size y (the book uses n) when x > 30 are taken from a population with mean μ and standard deviation σ, and if a sample mean x is computed for each sample, then… 1) The distribution of the sample means will be approximately normally distributed 2) The mean of the sampling distribution will be equal to the mean of the population μx = μ 3) The standard deviation of the sampling distribution will be equal to the standard deviation of the population divided by the square root of the number of items in each sample (y). The sample mean heights of random samples of the same population The hieghts of a population μx = μ μ σ

  3. There are two formulas used in this section and they are very similar to formulas we used in Chapter 7. y is the the number of items in the random sample

  4. How does the new part of the formula √x affect the z-score? Does this make sense? What happens to the z-score as x gets bigger? Does this make sense?

  5. The average purchase by a customer in a large novelty store is $4.00 with a standard deviation of $0.85. If 49 customers are selected at random, what is the probability that their average purchase will be less than $3.70? 0.4932 z = -2.47 Look this up in the columns in the chart. .0068 = 0.68% 0.5000 – 0.4932 = x = $3.70 μx= $4.00

  6. A trucking company has an average weight of 6000 pounds with a standard deviation of 120 pounds. 36 trucks are selected at random and their weights are recorded. Find the weight interval for the middle 90% of the averages of a sample size of 36. Look up 0.45 IN the chart. These are probabilities. 0.45 0.45 = 5967 = 6033 The middle 90% of the averages will lie between 5967 and 6033 pounds. μx= 6000

  7. From the HW P. 424 • An insurance company has customers that drive an average of 10,200 miles a year • with a standard deviation of 860 miles. A random survey of 49 customers is taken. • Find the probability that the average number of miles driven in the survey is between • 9,800 and 10,500 miles? 99.21%

  8. HW P. 424 #1-8 (You may want to try #7 and #8 before you leave class)

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