Central Limit Theorem

Topic Page

Questions

• What is the central limit theorem?
• What does independent and identically distributed mean?
• Why is sample size important when analyzing data?
• When does the Central Limit Theorem hold?
• A normally distributed population has a mean of 40 and a standard deviation of 12. What does the Central Limit Theorem say about the sampling distribution of the mean if samples of size 100 are drawn from this population?
• The heights of males in a certain country are normally distributed with a mean of 70.2 inches and a standard deviation of 4.2 inches. What is the probability that a randomly chosen male is under the height of 65 inches?
• How does the central limit theorem relate to hypothesis testing?
• What is the advantage of central limit theorem in sampling?
• How do you use the central limit theorem?
• Scores on a test are normally distributed with a mean of 68.2 and a standard deviation of 10.4. What is the probability that among 75 randomly selected students, at least 20 of them score greater than 78?
• What does the central limit theorem state?
• How do you find the mean and the standard deviation of the sampling distribution of ¯X and find an interval containing 95.44% of all possible sample mean returns?
• A sample of 50 values has a mean of 8.33 while the population standard deviation is 0.67. According to the Central Limit Theorem, the distribution of sample means is what?
• The population mean thickness of some wire is 12 mm with a standard deviation of .8 mm. A random sample of 100 pieces of wire is to be selected. What is the mean, variance and shape of this sample of 100 wires?
• What is the Central Limit Theorem used for?
• The probability that a seed will germinate is 0.34. Suppose 130 seeds are planted. How do you use the central limit theorem to determine the probability that at most 37 seeds germinate?