Answered: The lengths of bolts produced in a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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The lengths of bolts produced in a factory may be taken to be normally distributed. The botlts are checked on two "go-no go" gauges and those shorter tthan 2.9 or longer than 3.1 inches are rejected. A random sample of 397 bolts are checked on the gauges. If the (true but unknown) mean length of the bolts produced at that time was 3.06 inches and the (true but unknown) standard deviation was 0.03 inches, what values would you expect for n₁_, the number of bolts found to be too short, and n₂, the number of bolts found to be too long?

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.

Expert Solution

Step 1

Given :

$n = s a m p l e s i z e = 397$

$μ = m e a n = 3.06$

$σ = 0.03$ ( standard deviation)

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