Respuesta :
Answer:
The bolts with diameter less than 5.57 millimeters and with diameter greater than 5.85 millimeters should be rejected.
Step-by-step explanation:
We have been given that the diameters of bolts produced in a machine shop are normally distributed with a mean of 5.71 millimeters and a standard deviation of 0.08 millimeters.
Let us find the sample score that corresponds to z-score of bottom 4%.
From normal distribution table we got z-score corresponding to bottom 4% is -1.75 and z-score corresponding to top 4% or data above 96% is 1.75.
Upon substituting these values in z-score formula we will get our sample scores (x) as:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
[tex]-1.75=\frac{x-5.71}{0.08}[/tex]
[tex]-1.75*0.08=x-5.71[/tex]
[tex]-0.14=x-5.71[/tex]
[tex]-0.14+5.71=x-5.71+5.71[/tex]
[tex]5.57=x[/tex]
Therefore, the bolts with diameters less than 5.57 millimeters should be rejected.
Now let us find sample score corresponding to z-score of 1.75 as upper limit.
[tex]1.75=\frac{x-5.71}{0.08}[/tex]
[tex]1.75*0.08=x-5.71[/tex]
[tex]0.14=x-5.71[/tex]
[tex]0.14+5.71=x-5.71+5.71[/tex]
[tex]5.85=x[/tex]
Therefore, the bolts with diameters greater than 5.85 millimeters should be rejected.
