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A 3rd-party widget supplier for a key-component of the Tesla Model S manufactures widgets whose length follows a $N(\mu, 25mm) distribution. You take a sample of the widgets and measure their length.
How many widgets do you need to sample, to have a 95% confidence interval for with width 1mm?
The 95% confidence interval for the mean is:
$ x \pm z_0.025 * \frac{\sigma}{\sqrt(n)}
This has width
Setting the width equal to 1, and substituting and :
Thus,