Question

A company produces steel rods. The lengths of the steel rods are normally distributed with 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 bundled of 37 rods, find the probability that the average length is between 269.3-cm and 269.4-cm.

For part d), is the assumption of normal necessary? yes or no

Homework Answers

Answer #1

X ~ N(269.4, 1.4)
xbar ~ N(269.4, 1.4/sqrt(37)) = N(269.4, 0.2302)

c)
z = (x - μ)/σ
z1 = (269.3 - 269.4)/1.4 = -0.07
z2 = (269.4 - 269.4)/1.4 = 0

Therefore, we get
P(269.3 <= X <= 269.4) = P((269.4 - 269.4)/1.4) <= z <= (269.4 - 269.4)/1.4)
= P(-0.07 <= z <= 0) = P(z <= 0) - P(z <= -0.07)
= 0.5 - 0.4721
= 0.0279

d)
z = (x - μ)/σ
z1 = (269.3 - 269.4)/0.2302 = -0.43
z2 = (269.4 - 269.4)/0.2302 = 0

Therefore, we get
P(269.3 <= X <= 269.4) = P((269.4 - 269.4)/0.2302) <= z <= (269.4 - 269.4)/0.2302)
= P(-0.43 <= z <= 0) = P(z <= 0) - P(z <= -0.43)
= 0.5 - 0.3336
= 0.1664

e)
Yes

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A company produces steel rods. The lengths of the steel rods are normally distributed with a...
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...
A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 209.5-cm and a standard deviation of 1.1-cm. For shipment, 44 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...
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...
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...
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...
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...
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...
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...
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.
A company produces steel rods. The lengths of the steel rods are normally distributed with a...
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.