A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 133.5 cm and a standard deviation of 1.7 cm. For shipment, 19 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 steel rods is between 132.9 cm and 133.5 cm.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question

A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 133.5 cm and a standard deviation of 1.7 cm. For shipment, 19 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 steel rods is between 132.9 cm and 133.5 cm.

Expert Solution
Step 1

Given:

Population mean(μ=133.5Population standard deviationσ=1.7Sample size(n) = 19

Consider X is the random variable that is following the normal distribution with mean = 133.5 and standard deviation = 1.7

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Hypothesis Tests and Confidence Intervals for Means
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.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman