The Central Limit Theorem says A. When n>30n>30, the sampling distribution of x¯¯¯x¯ will be approximately a normal distribution. B. When n<30n<30, the original population will be approximately a normal distribution. C. When n>30n>30, the original population will be approximately a normal distribution. D. When n<30n<30, the sampling distribution of x¯¯¯x¯ will be approximately a normal distribution. E. None of the above

The Central Limit Theorem says A. When n>30n>30, the sampling distribution of x¯¯¯x¯ will be approximately a normal distribution. B. When n<30n<30, the original population will be approximately a normal distribution. C. When n>30n>30, the original population will be approximately a normal distribution. D. When n<30n<30, the sampling distribution of x¯¯¯x¯ will be approximately a normal distribution. E. None of the above

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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A variable of a population has a mean of u 200 and a standard deviation of o = 42. a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration? A. No assumption was made. B. Normal distribution. C. Uniform distribution. c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not? A. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true. O B. Yes, the sampling distribution of the sample mean is always normal. and standard deviation C. No, the sampling distribution of the sample mean is never normal for sample size less than 30.
Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 117 pounds and a standard deviation of 39.4 pounds. Random samples of size 15 are drawn from this population and the mean of each sample is determined. 4-0 0 = (Round to three decimal places as needed.) Sketch a graph of the sampling distribution. Choose the correct graph below. O A. A 96.7 117 137.3 Q O B. A 340.8 10.2 361.2 Q Q ww ^ A -106.8 10.2 127.2 86.5 117 147.5 O C. O D. Q
Q2. The sampling distribution of means tends toward Normality only when the underlying populations is Normal. This is true of Central Limit Theorem. TrueB. FalseC. None of the above
Is it possible for the 50th percentile of a distribution to be equal to the 60th percentile? Why or why not? A. No, because you won’t get the same result multiplying by 50 as you do by 60. B. No, because there will always be some values of the distribution in between the 50th and 60th percentiles. C. Yes, this can happen if the distribution is uniform. D. Yes, this can happen if there are many members of the population with the same value.
Which of the following are true? There is more than one correct answer.
Suppose a sample of size n is drawn from a population where the population standard deviation is known. In order to use the Central Limit Theorem, we would have to know that A n > 30 B The population is normally distributed. C n > 30 OR the population is normally distributed D n > 30 AND the population is normally distributed
Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally distributed, with a mean of 113 pounds and a standard deviation of 37.7 pounds. Random samples of size 20 are drawn from this population and the mean of each sample is determined.
Which of the following statements about Chebyshev's theorem is correct? B. Chebyshev's theorem states that all data points lie within three standard deviations of the mean in A. Chebyshev's theorem is only applicable to discrete distributions. any distribution. C. Chebyshev's theorem applies only to positively skewed distributions. D. Chebyshev's theorem applies to any distribution, regardless of its shape. E. Chebyshev's theorem is limited to normal distributions only. F. Chebyshev's theorem guarantees that at least 75% of data lie within three standard deviations of the mean in any distribution. 6. If a data set has a standard deviation of 18 and mean of 70, according to Chebyshev's theorem, what is the interval that must contain at least 19% of the data? A 50 to 90 3 B. 55 to 85 C. 20 to 80 D. 40 to 60 E. 35 to 65 F. None of the above Fina
Which of the following is the best statement of the Law of Large Numbers? If the parent population (from which the data are drawn) is normally distributed, then the sample mean, , will follow a normal distribution. For bell-shaped data, approximately 68% of the data will be within one standard deviation of the mean, about 95% of the data will be within two standard deviations of the mean, and approximately 99.7% of the data will be within three standard deviations of the mean. If the sample size is large, the sample mean will be close to the population mean µ If the sample size is large, the shape of the sampling distribution of the sample mean will be approximately normal.
1. The amount of time a train is late is Uniformly Distributed with a minimum of 2 minutes and a maximum of 27 minutes. Let X be the amount of time the train is late on a particular day. a. Find the mean of X and the standard deviation of X b. Find the probability that the train is more than 6 minutes late. c. Find the 90th percentile of X d. If the train is already 6 minutes late, find the probability that it will be more than 12 minutes late. e. Find the probability that the train will be less than 20 minutes late given that it is at least 5 minutes late.