The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness(x)has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determiningx,the mean coating thickness for the sample. (a)Describe the sampling distribution ofxfor a random sample of size 16.The distribution of x is with mean mm and standard deviation 0.0125 mm.(b)When no unusual circumstances are present, we expectxto be within2? xof 3 mm, the desired value. Anxvalue farther from 3 mm than2? xis interpreted as an indication of a problem that needs attention. Calculate3 ± 2? x.3 − 2? x= mm3 + 2? x= mm(c)Referring to part (b), what is the probability that a sample mean will be outside3 ± 2? xjust by chance (that is, when there are no unusual circumstances)? (Round your answer to four decimal places.)

Sampling distribution describe the sample probability follows an method. It is based on the sample…

Answered: The thickness (in millimeters) of 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

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The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness

(x)

has a normal distribution with a mean of 3 mm and a standard deviation of 0.05 mm. Suppose that the process will be monitored by selecting a random sample of 16 drives from each shift's production and determining

the mean coating thickness for the sample.

(a)

Describe the sampling distribution of

for a random sample of size 16.

The distribution of x is with mean mm and standard deviation 0.0125 mm.

(b)

When no unusual circumstances are present, we expect

to be within

2? _x

of 3 mm, the desired value. An

value farther from 3 mm than

2? _x

is interpreted as an indication of a problem that needs attention. Calculate

3 ± 2? _x.

3 − 2? _x

= mm

3 + 2? _x

= mm

(c)

Referring to part (b), what is the probability that a sample mean will be outside

3 ± 2? _x

just by chance (that is, when there are no unusual circumstances)? (Round your answer to four decimal places.)

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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