Answered: ii. Calculate the probability that the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

Steel rods manufactured in a plant must be a minimum of 2 metres in length in order to pass through an inspection procedure. Steel rods with lengths that are normally distributed, with a mean of 2.1 metres and a standard deviation of 0.1 metres, are produced during the manufacturing process. A random sample of 25 steel rods is chosen, and their lengths are measured using a tape measure.

i. Decide on the appropriate distribution of the sample mean of the 25 steel rods in the sample using the appropriate distribution formula.

ii. Calculate the probability that the sample mean of steel rods that meet the minimum length requirement is the same as the mean of the entire sample.

iii. For example, if the observed sample mean length of steel rods is 2.15, calculate the 98% two-sided confidence interval for the true mean length of the manufacturing process, assuming that it is not known.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution