5. The inside diameter of a randomly selected piston ring is a random variable with mean value of 15cm and standard deviation 0.05cm. (a) If X is the sample mean diameter for a random sample of n= 20 rings, what is the mean ofX, and what is the standard deviation of the X distribution? Round your answer to twodecimal places.(b) Answer the questions posed in part (a) for a sample size of n= 80 rings. Round your answerto 4 decimal places.(c) For which of the two random samples, the one from part (a) or the one from part (b), is Xmore likely to be within 0.01cm of 15 cm? Explain your reasoning.

Given: Inside diameter of ring = X μ = 15cm σ = 0.05cm

Answered: (a) If X is the sample mean diameter…

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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5. The inside diameter of a randomly selected piston ring is a random variable with mean value of 15cm and standard deviation 0.05cm.

(a) If X is the sample mean diameter for a random sample of n= 20 rings, what is the mean of
X, and what is the standard deviation of the X distribution? Round your answer to two
decimal places.
(b) Answer the questions posed in part (a) for a sample size of n= 80 rings. Round your answer
to 4 decimal places.
(c) For which of the two random samples, the one from part (a) or the one from part (b), is X
more likely to be within 0.01cm of 15 cm? Explain your reasoning.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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