Question

1.)A population of values has a normal distribution with μ=14
and σ=28. You intend to draw a random sample of size n=53

Find the probability that a single randomly selected value is
less than 22.5.

Find the probability that a sample of size n=53 is randomly
selected with a mean less than 22.5.

2.)A company produces steel rods. The lengths of the steel
rods are normally distributed with a mean of 149.3-cm and a
standard deviation of 1-cm. For shipment, 6 steel rods are bundled
together. Find P20, which is the average length separating the
smallest 20% bundles from the largest 80% bundles. p20=

3.)A company produces steel rods. The lengths of the steel
rods are normally distributed with a mean of 124.8-cm and a
standard deviation of 1.4-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 between 123.8-cm and
124.9-cm.

P(123.8-cm < M < 124.9-cm

4.)A company produces steel rods. The lengths of the steel
rods are normally distributed with a mean of 245.8-cm and a
standard deviation of 1.5-cm. For shipment, 17 steel rods are
bundled together. Find the probability that the average length of a
randomly selected bundle of steel rods is greater than
246.2-cm.

P(M > 246.2-cm

Answer #1

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 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 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 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) =

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 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 170.5-cm and a standard
deviation of 1.1-cm. For shipment, 12 steel rods are bundled
together. Find the probability that the average length of a
randomly selected bundle of steel rods is between 171-cm and
171.5-cm. P(171-cm < M < 171.5-cm) = Enter your answer as a
number accurate to 4 decimal places.

2.Assume that z-scores are normally distributed with a
mean of 0 and a standard deviation of 1.
If P(z>d)=0.8689P(z>d)=0.8689, find d.
3.A company produces steel rods. The lengths of the steel rods
are normally distributed with a mean of 247.5-cm and a standard
deviation of 1.9-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 between 247.2-cm and 248.6-cm.
P(247.2-cm < M < 248.6-cm) =

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 207.9-cm and a standard
deviation of 1.5-cm. For shipment, 26 steel rods are bundled
together.
Find P26,
which is the average length separating the smallest 26% bundles
from the largest 74% bundles.

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