Question

A machine produces bolts with a mean thread diameter of 0.250 inch and a standard deviation of 0.002Inch. Any bolts with a thread diameter greater than 0.250 inch or less than 0.244 inch must be rejected.What is the probability that a bolt produced by the machine will be rejected? Complete the explanationfor how you know34% 34%0.15% 2.35%2.35% 0.15%113.59613.5%18:10X20X 30The probability that a bolt produced by the machine will be rejected is %. The least possiblethread diameter is standard deviations from the mean. All values greater than the mean resultin a bolt whose threads are too large, so % of the bolts will be rejected for having threads toolarge in diameter.

Answer 1

EXPLANATION

As we have a normal distribution, we need to apply the following relationship:

`P(0.244We need to find the z-score:[tex]z=(x-\mu)/(\sigma)`

Where u=mean=0.250 and standard deviation=sigma=0.002

Replacing terms:

`z=(0.244-0.250)/(0.002)=-3`
`z=(0.250-0.250)/(0.002)=0`

So, the values of z should be between -3 and :

`P(-3\le x\le0)`

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

`P(\text{rejected)}=1-0.49865=0.50135`

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.