Answered: A manufacturer of car batteries claims…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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Question

A manufacturer of car batteries claims that the batteries will last, on
average, 3 years with a variance of 1 year. Seven of these batteries have
lifetimes, in years, as follows
1.9, 2.4, 3.0, 3.5, 4.2, 5.1, and 11.24
Construct a 99% confidence interval for σ² . Assume the population of
battery lives to be approximately normally distributed. Solve with proper solution

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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