Steel rods are manufactured with a mean length of 30centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.07 cm. Complete parts (a) to (d). Steel rods are manufactured with a mean length of 30 centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximatelynormally distributed with a standard deviation of 0.07 cm. Complete parts (a) to (d).(a) What proportion of rods has a length less than 29.9 cm?(Round to four decimal places as needed.)(b) Any rods that are shorter than 29.83 cm or longer than 30.17 cm are discarded. What proportion of rods will be discarded?(Round to four decimal places as needed.)(c) Using the results of part (b), if 5000 rods are manufactured in a day, how many should the plant manager expect to discard?(Use the answer from part b to find this answer. Round to the nearest integer as needed.)(d) If an order comes in for 10,000 steel rods, how many rods should the plant manager expect to manufacture if the order states that all rods must be between 29.9 cmand 30.1 cm?(Round up to the nearest integer.)

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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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Steel rods are manufactured with a mean length of 30centimeter (cm). Because of variability in the manufacturing process, the lengths of the rods are approximately normally distributed with a standard deviation of 0.07 cm. Complete parts (a) to (d).

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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