6 cm. th of a randomly selected steel rod is
MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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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 130.9 cm and a standard deviation of 0.6 cm.
Find the probability that the length of a randomly selected steel rod is between 129.5 cm and 129.8 cm.
\[
P(129.5 \text{ cm} < x < 129.8 \text{ cm}) = P(\_\_\_ < z < \_\_\_) \]
Shade: Between two values. Click and drag the arrows to adjust the values.
The diagram below is a normal distribution curve, depicted as a bell-shaped graph in blue. The horizontal axis is a standard normal distribution scale (z-scale) ranging approximately from -3 to 4. The shaded area between the blue arrows represents the probability of the specified range. The values of -2.4 and 2.1 mark the z-scores at which the area is shaded.
The "Submit Question" button below suggests that this is an interactive element where students can input their solution and check their understanding of the concept.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe9d5342c-147b-4a34-a8f5-3ca9ddac2bd5%2F3aecc66c-a305-4bf0-8388-ae1ec6de66bf%2Fvpu9q7.jpeg&w=3840&q=75)
Transcribed Image Text:A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 130.9 cm and a standard deviation of 0.6 cm.
Find the probability that the length of a randomly selected steel rod is between 129.5 cm and 129.8 cm.
\[
P(129.5 \text{ cm} < x < 129.8 \text{ cm}) = P(\_\_\_ < z < \_\_\_) \]
Shade: Between two values. Click and drag the arrows to adjust the values.
The diagram below is a normal distribution curve, depicted as a bell-shaped graph in blue. The horizontal axis is a standard normal distribution scale (z-scale) ranging approximately from -3 to 4. The shaded area between the blue arrows represents the probability of the specified range. The values of -2.4 and 2.1 mark the z-scores at which the area is shaded.
The "Submit Question" button below suggests that this is an interactive element where students can input their solution and check their understanding of the concept.
Expert Solution
Step 1
Let the random variable x denotes the length of the steel rods.
The length of the steel rods is normally distributed with a mean of 130.9 cm and a standard deviation of 0.6 cm
That is,
=130.9 and =0.6
Compute the probability that a randomly selected steel rod lies between 129.5 and 129.8
That is, P(129.5< x<129.8)
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