Question

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 179.5-cm and a standard
deviation of 0.7-cm. For shipment, 20 steel rods are bundled
together.

Find *P*_{95}, which is the average length
separating the smallest 95% bundles from the largest 5%
bundles.

*P*_{95} = -cm

Enter your answer as a number accurate to 2 decimal place. Answers
obtained using exact *z*-scores or *z*-scores rounded
to 3 decimal places are accepted.

Answer #1

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 179.5-cm and a standard
deviation of 0.7-cm. For shipment, 20 steel rods are bundled
together.

Find *P*_{95}, which is the average length
separating the smallest 95% bundles from the largest 5%
bundles.

*P*_{95} = -cm

Enter your answer as a number accurate to 2 decimal place. Answers
obtained using exact *z*-scores or *z*-scores rounded
to 3 decimal places are accepted.

Standard error = sd/ sqrt(n) = 0.7/sqrt(20) = 0.156525 = 0.1565 ( four decimals)

Z value for 95^{th} percentile=1.645

The required x= mean+z*sd = 179.5+1.645*0.1565 =179.7574

**=179.76 ( two decimals)**

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 197.5-cm and a standard
deviation of 2-cm. For shipment, 6 steel rods are bundled
together.
Find P11, which is the average length separating the smallest
11% bundles from the largest 89% bundles.
P11 =______________ -cm
Enter your answer as a number accurate to 2 decimal place.
Answers obtained using exact z-scores or z-scores rounded to 3
decimal places are accepted.

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 216.5-cm and a standard
deviation of 2.3-cm. For shipment, 24 steel rods are bundled
together.
Find P15, which is the average length
separating the smallest 15% bundles from the largest 85%
bundles.
P15 = -cm
Enter your answer as a number accurate to 2 decimal place. Answers
obtained using exact z-scores or z-scores rounded
to 3 decimal places are accepted.

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 252.7-cm and a standard
deviation of 2.4-cm. For shipment, 9 steel rods are bundled
together.
Find P82, which is the average length
separating the smallest 82% bundles from the largest 18%
bundles.
P82 = -cm
Enter your answer as a number accurate to 2 decimal place. Answers
obtained using exact z-scores or z-scores rounded
to 3 decimal places are accepted.

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 225.1-cm and a standard
deviation of 1.3-cm. For shipment, 10 steel rods are bundled
together. Find P95, which is the average length separating the
smallest 95% bundles from the largest 5% bundles. P95 = _____-cm
Enter your answer as a number accurate to 2 decimal place.

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.

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 237.4-cm and a standard
deviation of 1.6-cm. For shipment, 6 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is between 237.5-cm and 239.1-cm.
P(237.5-cm < M < 239.1-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers
obtained using exact z-scores or z-scores rounded
to 3...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 215.6-cm and a standard
deviation of 2.4-cm. For shipment, 15 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is between 215-cm and 216.5-cm.
P(215-cm < M < 216.5-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers
obtained using exact z-scores or z-scores rounded
to 3...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 179-cm and a standard deviation
of 2.4-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 less than 177.8-cm.
P(M < 177.8-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers
obtained using exact z-scores or z-scores rounded
to 3 decimal places are...

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normally distributed with a mean of 246.7-cm and a standard
deviation of 0.8-cm. For shipment, 23 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is greater than 246.6-cm.
P(M > 246.6-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers
obtained using exact z-scores or z-scores rounded
to 3 decimal places are...

A company produces steel rods. The lengths of the steel rods are
normally distributed with a mean of 122.8-cm and a standard
deviation of 0.6-cm. For shipment, 6 steel rods are bundled
together.
Find the probability that the average length of a randomly selected
bundle of steel rods is less than 122.7-cm.
P(M < 122.7-cm) =
Enter your answer as a number accurate to 4 decimal places. Answers
obtained using exact z-scores or z-scores rounded
to 3 decimal places are...

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