Question

A production process for steel rods used to reinforce concrete is known to produce rods whose lengths have a variance of 64 cm. The production machinery has been set to produce rods with a mean of (600 centimeters, cm), in length. These rods are tied into bundles of 40 for shipment to construction sites.

What is the probability that the average length of a randomly selected bundle is less than 598 cm?

What is the probability that the average length of a randomly selected bundle is more than 601 cm but less than 603 cm?

Answer #1

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 110.9-cm and a standard
deviation of 0.6-cm. For shipment, 7 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is less than 110.9-cm.
P(M < 110.9-cm) = ______________
Enter your answer as a number accurate to 4 decimal places.

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 129.2-cm and a standard
deviation of 0.5-cm. For shipment, 27 steel rods are bundled
together. Find the probability that the average length of a
randomly selected bundle of steel rods is greater than 129.3-cm.
P(M > 129.3-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.

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 98.8 cm and a standard
deviation of 2.5 cm. For shipment, 22 steel rods are bundled
together.
Note: Even though our sample size is less than 30, we can use
the z score because
1) The population is normally distributed and
2) We know the population standard deviation, sigma.
Find the probability that the average length of a randomly selected
bundle of...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 263.6 cm and a standard
deviation of 0.5 cm. For shipment, 27 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is less than 263.6 cm.
P(¯xx¯ < 263.6 cm) =
Enter your answer as a number accurate to 4 decimal places. Answers
should be obtained using zz scores rounded to...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 245.7-cm and a standard
deviation of 1.8-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 between 245.1-cm and
248.2-cm.
P(245.1-cm < M < 248.2-cm) =

1. A company produces steel rods. The lengths of the steel rods
are normally distributed with a mean of 116.7-cm and a standard
deviation of 1.8-cm. For shipment, 22 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is less than 116.8-cm.
P( x < 116.8-cm) =
2. CNNBC recently reported that the mean annual cost of auto
insurance is 1010 dollars. Assume the standard deviation is 216
dollars....

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