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Let x denote the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean value and standard deviation of x are μ = 2 minutes and 0.5 minutes, respectively. (a) If x is the sample mean time for a random sample of n=9 students, where is the sampling distribution of x centered, and how much does it spread out around the center (as described by its standard deviation)? (Round your answers to three decimal places minutes minutes ox (b) Repeat part (a) for a sample of size of n 40 and again for a sample of size n 100. (Round your answers to three decimal places.) n-40 ox- n - 100 minutes minutes minutes minutes How do the centers and variability of the three distributions compare to one another? The centers of the distributions of the sample mean are --Select-- ✓, and the standard deviations (and therefore spreads) these distributions are -Select-- (c) Which of the sample sizes in part (b) would be most likely to result in an x value close to u, and why? A sample size of n=--Select-- is most likely to result in a sample mean close to μ, since this is the sample size that results in the ---Select--- of the distribution of X.

Let x denote the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean value and standard deviation of x are μ = 2 minutes and 0.5 minutes, respectively. (a) If x is the sample mean time for a random sample of n=9 students, where is the sampling distribution of x centered, and how much does it spread out around the center (as described by its standard deviation)? (Round your answers to three decimal places minutes minutes ox (b) Repeat part (a) for a sample of size of n 40 and again for a sample of size n 100. (Round your answers to three decimal places.) n-40 ox- n - 100 minutes minutes minutes minutes How do the centers and variability of the three distributions compare to one another? The centers of the distributions of the sample mean are --Select-- ✓, and the standard deviations (and therefore spreads) these distributions are -Select-- (c) Which of the sample sizes in part (b) would be most likely to result in an x value close to u, and why? A sample size of n=--Select-- is most likely to result in a sample mean close to μ, since this is the sample size that results in the ---Select--- of the distribution of X.

A First Course in Probability (10th Edition)
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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Let x denote the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean value and standard deviation of x are μ = 2 minutes and = 0.5 minutes, respectively. (a) If x is the sample mean time for a random sample of n = 9 students, where is the sampling distribution of X centered, and how much does it spread out around the center (as described by its standard deviation)? (Round your answers to three decimal places.) HJ minutes minutes ox= (b) Repeat part (a) for a sample of size of n = 40 and again for a sample of size n = 100. (Round your answers to three decimal places.) n = 40 H= = n = 100 μ== ox= minutes minutes minutes minutes How do the centers and variability of the three x distributions compare to one another? The centers of the distributions of the sample mean are ---Select--- ✓, and the standard deviations (and therefore spreads) of these distributions are ---Select--- (c) Which of the sample sizes in part (b) would be most likely to result in an x value close to μ, and why? A sample size of n = ---Select--- is most likely to result in a sample mean close to u, since this is the sample size that results in the ---Select--- of the distribution of X.
Transcribed Image Text:Let x denote the time (in minutes) that it takes a fifth-grade student to read a certain passage. Suppose that the mean value and standard deviation of x are μ = 2 minutes and = 0.5 minutes, respectively. (a) If x is the sample mean time for a random sample of n = 9 students, where is the sampling distribution of X centered, and how much does it spread out around the center (as described by its standard deviation)? (Round your answers to three decimal places.) HJ minutes minutes ox= (b) Repeat part (a) for a sample of size of n = 40 and again for a sample of size n = 100. (Round your answers to three decimal places.) n = 40 H= = n = 100 μ== ox= minutes minutes minutes minutes How do the centers and variability of the three x distributions compare to one another? The centers of the distributions of the sample mean are ---Select--- ✓, and the standard deviations (and therefore spreads) of these distributions are ---Select--- (c) Which of the sample sizes in part (b) would be most likely to result in an x value close to μ, and why? A sample size of n = ---Select--- is most likely to result in a sample mean close to u, since this is the sample size that results in the ---Select--- of the distribution of X.
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