Answered: Question 3 Please answer only a) and…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question 3

Please answer only a) and b)

From a new boulangerie in Cologne's Südstadt district it is known that the baguette weight (in grams) is normally distributed with an unknown expected value μ and a theoretical standard deviation of 5.10 grams. For a sample of size 16 to examine the mean baguette weight results in an average weight of 249.54 grams.

a) Determine a specific confidence interval for the expected value of the baguette weight at the confidence level 0.97 and state the length of this interval.

b) What is the minimum size of the sample so that a confidence interval for the expected value of the baguette weight at the confidence level 0.97 has a length of at most 2.5 grams?

c) How does the length of the confidence interval from sub-task a) change (with the same sample) if the confidence level is lowered to 0.92?

d) It is also known that the weight of baguettes (in grams) from a second boulangerie is also normally distributed in the village, whereby both parameters μ and σ are unknown here. For this boulangerie, a size 35 sample found an average baguette weight of 248.21 grams and a sample standard deviation of 6.24 grams. Also determine a specific confidence interval for the expected value of the baguette weight of this second boulangerie, also here at the confidence level 0.97, and interpret the obtained confidence interval.

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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