Answered: If a population has a standard…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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For nos. 8 to 12: Answer the ff. 8. If a population has a standard deviation of 9.7, what is the standard deviation of the sampling distribution of its means? The sampling distribution was derived with sample size n = 16. 9. Which of the following is the reason why the sampling distribution of the sample mean is a normal distribution? a. The variance of the population is small. b. The sample size is large. C. The sample is taken from a normal population. d. The Central Limit Theorem guarantees that the sampling distribution of the sample mean is normal regardless of the distribution of the population where the sample was taken. 10. Consider a population consisting of values 2, 3, 5, 7. What is the population standard deviation? 11. Which of the following statements is NOT true about the Central Limit Theorem? a. When a population does not have a normal distribution, the distribution of the sample means will approximately be normal if a large number of samples is taken. b. When the population has a normal distribution, the distribution of the sample means will be uniform for any sample size. C. The larger the sample size from a population is, the better the approximation of a normal distribution. d. The Central Limit Theorem allows us to answer questions about sample means using the normal distribution, even if the population is not normal. 12. Suppose that a population consists of the values 1, 2, 3, 4, 5, and 6. Samples of size 2 are taken with replacement from this population. How many samples of size two are possible?

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.

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