EXPLANATION
As we have a normal distribution, we need to apply the following relationship:
[tex]P(0.244We need to find the z-score:[tex]z=\frac{x-\mu}{\sigma}[/tex]Where u=mean=0.250 and standard deviation=sigma=0.002
Replacing terms:
[tex]z=\frac{0.244-0.250}{0.002}=-3[/tex][tex]z=\frac{0.250-0.250}{0.002}=0[/tex]So, the values of z should be between -3 and :
[tex]P(-3\le x\le0)[/tex]Now, we need to use the z-table to compute these values of z-score:
P(z= -3)= 0.00135
P(z= 0)= 0,50
Subtraction both terms give us the probability that the values would be between 0.244 and 250:
0.50 - 0.00135 = 0.49865
The probability that the bolts would be rejected is the difference between 1 and the obtained probability
[tex]P(\text{rejected)}=1-0.49865=0.50135[/tex]Answer: The probability that a bolt produced by the machine will be rejected is 50.13%
The least possible thread diameter is 3 standard deviations from the mean.
All values greater than the mean result in a bolt whose threads are too large, so 50% of the bolts will be rejected for having threads too large in diameter.