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Published byChristian Walters Modified over 9 years ago
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Chapter 7 The Normal Probability Distribution 7.3 Applications of the Normal Distribution
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EXAMPLE Finding the Area Under a Normal Curve It is known that the length of a certain steel rod is normally distributed with a mean of 100 cm and a standard deviation of 0.45 cm. * What is the probability that a randomly selected steel rod has a length less than 99.2 cm? * Based upon information obtained from Stefan Wilk.
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EXAMPLE Finding the Area Under a Normal Curve It is known that the length of a certain steel rod is normally distributed with a mean of 100 cm and a standard deviation of 0.45 cm. What is the probability that a randomly selected steel rod has a length between 99.8 and 100.3 cm?
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EXAMPLE Finding the Area Under a Normal Curve It is known that the length of a certain steel rod is normally distributed with a mean of 100 cm and a standard deviation of 0.45 cm. Suppose the manufacturer must discard all rods less than 99.1 cm or longer than 100.9 cm. What proportion of rods must be discarded?
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EXAMPLE Finding the Area Under a Normal Curve It is known that the length of a certain steel rod is normally distributed with a mean of 100 cm and a standard deviation of 0.45 cm. Find the length corresponding to the 35th percentile.
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EXAMPLE Finding the Area Under a Normal Curve It is known that the length of a certain steel rod is normally distributed with a mean of 100 cm and a standard deviation of 0.45 cm. Suppose the manufacturer wants to accept 90% of all rods manufactured. Determine the length of rods that make up the middle 90% of all steel rods manufactured.
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