A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 237-cm and a standard deviation of 2.5-cm. For shipment, 16 steel rods are bundled together. Round all answers to four decimal places if necessary.What is the distribution of XX? XX ~ N(,)What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)For a single randomly selected steel rod, find the probability that the length is between 237.3-cm and 237.7-cm. For a bundled of 16 rods, find the probability that the average length is between 237.3-cm and 237.7-cm. For part d), is the assumption of normal necessary? YesNo

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Answered: A company produces steel rods. The…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 237-cm and a standard deviation of 2.5-cm. For shipment, 16 steel rods are bundled together. Round all answers to four decimal places if necessary.

What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For a single randomly selected steel rod, find the probability that the length is between 237.3-cm and 237.7-cm.
For a bundled of 16 rods, find the probability that the average length is between 237.3-cm and 237.7-cm.
For part d), is the assumption of normal necessary? YesNo

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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