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andreev551 [17]
3 years ago
5

Your manufacturing company sells metal nuts and bolts that come together in a package. The diameter of the bolts coming off the

factory line follows a normal distribution with mean 18mm and standard deviation 0.1mm. The diameters of the holes in the nuts follow a normal distribution with mean 18.7mm and standard deviation of 0.08mm. Assume that in order for a nut and bolt to fit together the diameter of the hole in the nut has to be between .5 and .9 mm larger than the bolt. Find the z score for bolt of 18.12 mm.
Mathematics
1 answer:
Reil [10]3 years ago
5 0

Answer:

The z score for bolt of diameter 18.12 mm is 1.20.

Step-by-step explanation:

Let <em>X</em> = diameter of bolts.

It is provided that the random variable <em>X</em> follows a Normal distribution with mean, <em>μ</em> = 18 mm and standard deviation, <em>σ</em> = 0.10 mm.

A <em>z</em>-score is a standardized score, a numerical, that defines how far a data value from the mean.

The distribution of <em>z</em>-scores is defined by the Standard Normal distribution.

Z\sim N(0, 1)

The formula to compute the <em>z</em>-score is:

z=\frac{x-\mu}{\sigma}

The value of the diameter of a bolt is, <em>x</em> = 18.12 mm.

Compute the <em>z</em>-score for this value as follows:

z=\frac{x-\mu}{\sigma}=\frac{18.12-18}{0.10}=\frac{0.12}{0.10}=1.20

Thus, the z score for bolt of diameter 18.12 mm is 1.20.

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