The diameters of bolts produced in a machine shop are normally distributed with a mean of 5.61 millimeters and a standard deviation of 0.04 millimeters. find the two diameters that separate the top 7% and the bottom 7%. these diameters could serve as limits used to identify which bolts should be rejected. round your answer to the nearest hundredth, if necessary.

The two diameters that separate the top 7% and the bottom 7% are 5.6692 mm and 5.5508 mm respectively .

Step-by-step explanation:

Given :Mean = 5.61 millimeters

           Standard deviation = 0.04 millimeters.

To Find : Find the two diameters that separate the top 7% and the bottom 7%

Solution :

Case 1

We need to find such that

Refer the z table for z value

So, z corresponding to p = 0.97 is 1.48

Formula :

So, the diameter that separate the top 7% is

Case 2)

We need to find such that

Refer the z table for z value

So, z corresponding to p = 0.07 is -1.48

Formula :

So, the diameter that separate the bottom 7% is

Hence  the two diameters that separate the top 7% and the bottom 7% are 5.6692 mm and 5.5508 mm respectively .

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl