Answered: a shampoo knows that customers like…

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

The maker of a shampoo knows that customers like
this product to have a lot of foam. Ten sample bottles of the
product are selected at random and the foam heights observed
are as follows (in millimeters): 210, 215, 194, 195, 211, 201,
198, 204, 208, and 196.
(a) Is there evidence to support the assumption that foam
height is normally distributed?
(b) Find a 95% CI on the mean foam height.
(c) Find a 95% prediction interval on the next bottle of shampoo that will be tested.
(d) Find an interval that contains 95% of the shampoo foam
heights with 99% confidence.
(e) Explain the difference in the intervals computed in parts
(b), (c), and (d).

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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