Lazurus Steel Corporation produces iron rods that are supposed to be 30 inches long. The machine that makes these rods does not produce each rod exactly 30 inches long. The lengths of the rods vary slightly. It is known that when the machine is working properly, the mean length of the rods made on this machine is 30 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.3 inch. The quality control department takes a sample of 21 such rods every week, calculates the mean length of these rods, and makes a 97% confidence interval for the population mean. If either the upper limit of this confidence interval is greater than 30.10 inches or the lower limit of this confidence interval is less than 29.9 inches, the machine is stopped and adjusted. A recent sample of 21 rods produced a mean length of 30.01 inches. Based on this sample, will you conclude that the machine needs an adjustment? Assume that the lengths of all such rods have a normal distribution. Round your answers to two decimal places. The confidence interval is to inches. The machine an adjustment.
Lazurus Steel Corporation produces iron rods that are supposed to be 30 inches long. The machine that makes these rods does not produce each rod exactly 30 inches long. The lengths of the rods vary slightly. It is known that when the machine is working properly, the mean length of the rods made on this machine is 30 inches. The standard deviation of the lengths of all rods produced on this machine is always equal to 0.3 inch. The quality control department takes a sample of 21 such rods every week, calculates the mean length of these rods, and makes a 97% confidence interval for the population mean. If either the upper limit of this confidence interval is greater than 30.10 inches or the lower limit of this confidence interval is less than 29.9 inches, the machine is stopped and adjusted. A recent sample of 21 rods produced a mean length of 30.01 inches. Based on this sample, will you conclude that the machine needs an adjustment? Assume that the lengths of all such rods have a normal distribution. Round your answers to two decimal places. The confidence interval is to inches. The machine an adjustment.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.5: Comparing Sets Of Data
Problem 13PPS
Related questions
Concept explainers
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Topic Video
Question
Transcribed Image Text:Lazurus Steel Corporation produces iron rods that are supposed to be 30 inches long. The machine that makes these rods does not produce each rod exactly 30 inches
long. The lengths of the rods vary slightly. It is known that when the machine is working properly, the mean length of the rods made on this machine is 30 inches. The
standard deviation of the lengths of all rods produced on this machine is always equal to 0.3 inch. The quality control department takes a sample of 21 such rods
every week, calculates the mean length of these rods, and makes a 97% confidence interval for the population mean. If either the upper limit of this confidence
interval is greater than 30.10 inches or the lower limit of this confidence interval is less than 29.9 inches, the machine is stopped and adjusted. A recent sample of 21
rods produced a mean length of 30.01 inches. Based on this sample, will you conclude that the machine needs an adjustment? Assume that the lengths of all such
rods have a normal distribution.
Round your answers to two decimal places.
The confidence interval is
to
inches.
The machine
an adjustment.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt