A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 211.4- cm and a standard deviation of 1-cm. For shipment, 35 steel rods are bundled together. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( b. What is the distribution of x? - N( c. For a single randomly selected steel rod, find the probability that the length is between 211.2-cm and 211.5-cm. d. For a bundled of 35 rods, find the probability that the average length is between 211.2-cm and 211.5- cm. e. For part d), is the assumption of normal necessary? Yes No > Next Question
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 211.4- cm and a standard deviation of 1-cm. For shipment, 35 steel rods are bundled together. Round all answers to four decimal places if necessary. a. What is the distribution of X? X - N( b. What is the distribution of x? - N( c. For a single randomly selected steel rod, find the probability that the length is between 211.2-cm and 211.5-cm. d. For a bundled of 35 rods, find the probability that the average length is between 211.2-cm and 211.5- cm. e. For part d), is the assumption of normal necessary? Yes No > Next Question
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 211.4 cm and a standard deviation of 1 cm. For shipment, 35 steel rods are bundled together. Round all answers to four decimal places if necessary.
a. What is the distribution of \( X \)? \( X \sim N(\underline{\hspace{2cm}} , \underline{\hspace{2cm}}) \)
b. What is the distribution of \( \bar{x} \)? \( \bar{x} \sim N(\underline{\hspace{2cm}} , \underline{\hspace{2cm}}) \)
c. For a single randomly selected steel rod, find the probability that the length is between 211.2 cm and 211.5 cm. \(\underline{\hspace{2cm}}\)
d. For a bundled of 35 rods, find the probability that the average length is between 211.2 cm and 211.5 cm. \(\underline{\hspace{2cm}}\)
e. For part d), is the assumption of normal necessary?
\[
\begin{array}{c}
\text{Yes} \quad \bigcirc \\
\text{No} \quad \bigcirc
\end{array}
\]
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Transcribed Image Text:A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 211.4 cm and a standard deviation of 1 cm. For shipment, 35 steel rods are bundled together. Round all answers to four decimal places if necessary.
a. What is the distribution of \( X \)? \( X \sim N(\underline{\hspace{2cm}} , \underline{\hspace{2cm}}) \)
b. What is the distribution of \( \bar{x} \)? \( \bar{x} \sim N(\underline{\hspace{2cm}} , \underline{\hspace{2cm}}) \)
c. For a single randomly selected steel rod, find the probability that the length is between 211.2 cm and 211.5 cm. \(\underline{\hspace{2cm}}\)
d. For a bundled of 35 rods, find the probability that the average length is between 211.2 cm and 211.5 cm. \(\underline{\hspace{2cm}}\)
e. For part d), is the assumption of normal necessary?
\[
\begin{array}{c}
\text{Yes} \quad \bigcirc \\
\text{No} \quad \bigcirc
\end{array}
\]
[Next Question]
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