Question

a production process manufactures items with weights that are normally distributed with mean 17 pounds and standard deviation 0.1 pound. an item is considered to be defective if its weight is less than 16.85 pounds or greater than 17.15 pounds. suppose that these items are currently produced in batches of 500 units. a) (10 points) find the probability that an inspected item is defective. b) (10 points) find the probability that at most 10% of the items in a given batch will be defective. hint: find the probability that an item is defective using normal probabilities. then, you can model number of defectives out of 500 as binomial

Answer 1

The probability that at most 10% of the items in a given batch will be defective = 0.31333

We are aware that the item is broken.

Rate it 17.15 if X is either less than 16.85 or is.

Therefore, we simply found the area of one tail and multiplied it by two as we have seen their identical distance from the Min.

Therefore, let's choose 16.85.

We'll calculate a Z score for that.

Therefore, let's go on to the X value less the mean more than the standard deviation

This may be 16.85 -70, which will be 0.15 divided by.1 negative.

You will have a result of -1.5.

As a result, the Z distribution's region to the left of negative 1.5 will have a value of 0.0668. Divide that amount by two.

Z-score=0.0668/2=0.31333

You will also receive 0.31333.

To learn more about Z-score:

brainly.com/question/15016913

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