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(i). Find the probability that one randomly selected unit has a length greater than 120 cm. Keep two decimal places. (The answer would be 0.28. You can use the answer for the following questions even though If you cannot figure out how to get it.)

(i). Find the probability that one randomly selected unit has a length greater than 120 cm. Keep two decimal places. (The answer would be 0.28. You can use the answer for the following questions even though If you cannot figure out how to get it.)

MATLAB: An Introduction with Applications
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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An automated machine in a manufacturing process is operating properly if the length of an important component is normally distributed, with u = 117 cm and o = 5.2 cm. Show your work for the following questions. (i). Find the probability that one randomly selected unit has a length greater than 120 cm. Keep two decimal places. (The answer would be 0.28. You can use the answer for the following questions even though If you cannot figure out how to get it.) (ii). Suppose four units are randomly selected. What is the probability that no more than one unit has a length greater than 120 cm? (iii). Suppose one hundred units are randomly selected. What is the probability that at least twenty units have lengths greater than 120 cm? Use normal approximation for binomial distributions to answer this question. Keep four decimal places. Check if the requirements for normal approximation are met before you do any calculations. The exact value calculated from the binomial distribution is 0.9741. Is your answer from the normal approximation close?
Transcribed Image Text:An automated machine in a manufacturing process is operating properly if the length of an important component is normally distributed, with u = 117 cm and o = 5.2 cm. Show your work for the following questions. (i). Find the probability that one randomly selected unit has a length greater than 120 cm. Keep two decimal places. (The answer would be 0.28. You can use the answer for the following questions even though If you cannot figure out how to get it.) (ii). Suppose four units are randomly selected. What is the probability that no more than one unit has a length greater than 120 cm? (iii). Suppose one hundred units are randomly selected. What is the probability that at least twenty units have lengths greater than 120 cm? Use normal approximation for binomial distributions to answer this question. Keep four decimal places. Check if the requirements for normal approximation are met before you do any calculations. The exact value calculated from the binomial distribution is 0.9741. Is your answer from the normal approximation close?
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