Question

The lengths of the rods from a new cutting machine can be said to approximate a normal distribution with a mean of 10 meters and a standard deviation of 2 meters. Find the probability that a rod selected will have a length: a) of less than 10.0 meters, b) between 10.1 and 10.4 meters, c) greater than 9.9 meters

What should be the length of a rod such that the chance of producing rods longer than it is 2.5%

Answer #1

A company manufactures a large number of rods. The lengths of
the rods are normally distributed with a mean length of 4.4 inches
and a standard deviation of .5 inches. If you choose a rod at
random, what is the probability that the rod you chose will be:
a) Less than 4.5 inches?
b) Greater than 4.0 inches?
c) Between 3.8 inches and 4.7 inches?

A factory manufactures alloy rods for construction companies.
The lengths of rods are uniformly distributed with minimum of 90
and maximum of 110 cm.
A. Find the 80th percentile of the length of the rods.
B. Find the probability a rod is less than 101.4 cm long.
C. Find the probability a rod is more than 102.5 cm long.
D. Given that the rod is more than 101 cm, find the probability
it is longer than 99 cm.
E. Given...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 180.6-cm and a standard
deviation of 1-cm. For shipment, 11 steel rods are bundled
together. Round all answers to four decimal places if
necessary.
What is the distribution of X ? X ~ N( , )
What is the distribution of ¯ x ? ¯ x ~ N( , )
For a single randomly selected steel rod, find the probability
that the...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 214.4-cm and a standard
deviation of 0.6-cm. For shipment, 14 steel rods are bundled
together. Round all answers to four decimal places if
necessary.
What is the distribution of XX? XX ~ N(,)
What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
For a single randomly selected steel rod, find the probability
that the length is between 214.2-cm and 214.3-cm.
For a...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 269.4-cm and a standard
deviation of 1.4-cm. For shipment, 37 steel rods are bundled
together. Round all answers to four decimal places if
necessary.
What is the distribution of X? X ~ N
What is the distribution of ¯x? ¯x ~ N
For a single randomly selected steel rod, find the probability
that the length is between 269.3-cm and 269.4-cm.
For a...

1) A company produces steel rods. The lengths of the steel rods
are normally distributed with a mean of 183.4-cm and a standard
deviation of 1.3-cm.
Find the probability that the length of a randomly selected steel
rod is between 179.9-cm and 180.3-cm.
P(179.9<x<180.3)=P(179.9<x<180.3)=
2) A manufacturer knows that their items have a normally
distributed length, with a mean of 6.3 inches, and standard
deviation of 0.6 inches.
If 9 items are chosen at random, what is the probability that...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 91.1-cm and a standard
deviation of 0.5-cm. For shipment, 25 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is greater than 90.8-cm.
P(M > 90.8-cm) =

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 1.3-cm. For shipment, 5 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is greater than 211.5-cm.
P(M > 211.5-cm) =

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 226.6-cm and a standard
deviation of 1.7-cm. For shipment, 10 steel rods are bundled
together. Find the probability that the average length of a
randomly selected bundle of steel rods is less than 227.9-cm. P(M
< 227.9-cm) =

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 127.8-cm and a standard
deviation of 1.6-cm. For shipment, 16 steel rods are bundled
together. Find the probability that the average length of a
randomly selected bundle of steel rods is greater than 126.7-cm.
P(M > 126.7-cm) = Enter your answer as a number accurate to 4
decimal places.

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