Repeat Exercise 19 for samples of size 40 and 60. What happens to the mean and the standard deviation of the distribution of sample means as the sample size increases? Interpreting the Central Limit Theorem In Exercises 19–26, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution. 19. SAT Critical Reading Scores: Males The scores for males on the critical reading portion of the SAT in 2016 are normally distributed , with a mean of 495 and a standard deviation of 120. Random samples of size 20 are drawn from this population, and the mean of each sample is determined. (Source: The College Board)
Repeat Exercise 19 for samples of size 40 and 60. What happens to the mean and the standard deviation of the distribution of sample means as the sample size increases? Interpreting the Central Limit Theorem In Exercises 19–26, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution. 19. SAT Critical Reading Scores: Males The scores for males on the critical reading portion of the SAT in 2016 are normally distributed , with a mean of 495 and a standard deviation of 120. Random samples of size 20 are drawn from this population, and the mean of each sample is determined. (Source: The College Board)
Solution Summary: The author calculates the mean and standard deviation of the indicated sampling distribution of sample means for a sample of any size by using central limit theorem.
Repeat Exercise 19 for samples of size 40 and 60. What happens to the mean and the standard deviation of the distribution of sample means as the sample size increases?
Interpreting the Central Limit TheoremIn Exercises 19–26, find the mean and standard deviation of the indicated sampling distribution of sample means. Then sketch a graph of the sampling distribution.
19. SAT Critical Reading Scores: Males The scores for males on the critical reading portion of the SAT in 2016 are normally distributed, with a mean of 495 and a standard deviation of 120. Random samples of size 20 are drawn from this population, and the mean of each sample is determined. (Source: The College Board)
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.