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The inside diameter of a randomly selected piston ring is a random variable with mean value 14 cm and standard deviation 0.07 cm. (a) If X is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered and what is the standard deviation of the X distribution? (Enter your standard deviation to five decimal places.) center cm standard deviation cm (b) Answer the questions posed in part (a) for a sample size of n = 64 rings. (Enter your standard deviation to five decimal places.) center cm standard deviation cm (c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 0.01 cm of 14 cm? Explain your reasoning. O x is more likely to be within 0.01 cm of 14 cm in sample (a) because of the decreased variability with a smaller sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (b) because of the decreased variability with a larger sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (b) because of the increased variability with a larger sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (a) because of the increased variability with a smaller sample size.

The inside diameter of a randomly selected piston ring is a random variable with mean value 14 cm and standard deviation 0.07 cm. (a) If X is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered and what is the standard deviation of the X distribution? (Enter your standard deviation to five decimal places.) center cm standard deviation cm (b) Answer the questions posed in part (a) for a sample size of n = 64 rings. (Enter your standard deviation to five decimal places.) center cm standard deviation cm (c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 0.01 cm of 14 cm? Explain your reasoning. O x is more likely to be within 0.01 cm of 14 cm in sample (a) because of the decreased variability with a smaller sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (b) because of the decreased variability with a larger sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (b) because of the increased variability with a larger sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (a) because of the increased variability with a smaller sample size.

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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The inside diameter of a randomly selected piston ring is a random variable with mean value 14 cm and standard deviation 0.07 cm. (a) If X is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered and what is the standard deviation of the X distribution? (Enter your standard deviation to five decimal places.) center cm standard deviation cm (b) Answer the questions posed in part (a) for a sample size of n = 64 rings. (Enter your standard deviation to five decimal places.) center cm standard deviation cm (c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 0.01 cm of 14 cm? Explain your reasoning. O x is more likely to be within 0.01 cm of 14 cm in sample (a) because of the decreased variability with a smaller sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (b) because of the decreased variability with a larger sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (b) because of the increased variability with a larger sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (a) because of the increased variability with a smaller sample size.
Transcribed Image Text:The inside diameter of a randomly selected piston ring is a random variable with mean value 14 cm and standard deviation 0.07 cm. (a) If X is the sample mean diameter for a random sample of n = 16 rings, where is the sampling distribution of X centered and what is the standard deviation of the X distribution? (Enter your standard deviation to five decimal places.) center cm standard deviation cm (b) Answer the questions posed in part (a) for a sample size of n = 64 rings. (Enter your standard deviation to five decimal places.) center cm standard deviation cm (c) For which of the two random samples, the one of part (a) or the one of part (b), is X more likely to be within 0.01 cm of 14 cm? Explain your reasoning. O x is more likely to be within 0.01 cm of 14 cm in sample (a) because of the decreased variability with a smaller sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (b) because of the decreased variability with a larger sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (b) because of the increased variability with a larger sample size. O x is more likely to be within 0.01 cm of 14 cm in sample (a) because of the increased variability with a smaller sample size.
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