A company produces steel rods. The lengths of the steel rods are distributed with a mean of 102.3-cm and a standard deviation of 2-cm. For shipment, 7 steel rods are bundled together. Round all answers to four decimal places if necessary. Note: When writing the distributions, they should be of the form (mean, variance) a. What is the distribution of X? X~ ( b. What is the distribution of X? X ~ N( c. For a single randomly selected steel rod, find the probability that the length is between 102.5-cm and 103.5-cm.

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A company produces steel rods. The lengths of the steel rods are distributed with a mean of 102.3-cm and a
standard deviation of 2-cm. For shipment, 7 steel rods are bundled together.
Round all answers to four decimal places if necessary.
Note: When writing the distributions, they should be of the form (mean, variance)
a. What is the distribution of X?
X ~ (
b. What is the distribution of X?
X~ N(
c. For a single randomly selected steel rod, find the probability that the length is between 102.5-cm
and 103.5-cm.
d. For a bundled of 7 rods, find the probability that the average length is between 102.5-cm and 103.5-
cm.
e. For part d), is the assumption of normal necessary? Yes No
Transcribed Image Text:A company produces steel rods. The lengths of the steel rods are distributed with a mean of 102.3-cm and a standard deviation of 2-cm. For shipment, 7 steel rods are bundled together. Round all answers to four decimal places if necessary. Note: When writing the distributions, they should be of the form (mean, variance) a. What is the distribution of X? X ~ ( b. What is the distribution of X? X~ N( c. For a single randomly selected steel rod, find the probability that the length is between 102.5-cm and 103.5-cm. d. For a bundled of 7 rods, find the probability that the average length is between 102.5-cm and 103.5- cm. e. For part d), is the assumption of normal necessary? Yes No
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