A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Question
**Steel Rod Length Probability Calculation** A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 122.7 cm and a standard deviation of 0.5 cm. **Problem Statement:** Find the probability that the length of a randomly selected steel rod is between 122.8 cm and 123.2 cm. **Solution:** To find this probability, we will use the properties of the normal distribution and standard scores (z-scores). A z-score is calculated as follows: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \( X \) is the value, - \( \mu \) is the mean, - \( \sigma \) is the standard deviation. Calculate the z-scores for 122.8 cm and 123.2 cm, and use the standard normal distribution table to find the probability.
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Transcribed Image Text:**Steel Rod Length Probability Calculation** A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 122.7 cm and a standard deviation of 0.5 cm. **Problem Statement:** Find the probability that the length of a randomly selected steel rod is between 122.8 cm and 123.2 cm. **Solution:** To find this probability, we will use the properties of the normal distribution and standard scores (z-scores). A z-score is calculated as follows: \[ z = \frac{(X - \mu)}{\sigma} \] where: - \( X \) is the value, - \( \mu \) is the mean, - \( \sigma \) is the standard deviation. Calculate the z-scores for 122.8 cm and 123.2 cm, and use the standard normal distribution table to find the probability.
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