Answered: We find a new box that outputs numbers…

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

We find a new box that outputs numbers from a normal distribution X, but this time
we do not know what either the expected value or the standard deviation is.
This numbers are given with 4-digit accuracy:

16.8976

4.8728

18.5699

23.4441

17.4997

19.0779

17.4574

14.5035

15.8886

19.0164

11.3645

16.8926

13.7500

12.2102

15.0089

(a) Find a 95% confidence interval for the expected value of X.
(b) Find a 95% confidence interval for the standard deviation of X.
(c) Since each student gets different numbers, some students will get confidence intervals that do not contain the real expected value or the true standard deviation. About how many percent of submissions will get confidence intervals that miss expected value? On the standard deviation? On both?

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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