There is a population of millions of computer chips produced at a factory. The production process is so precious that it is known that the population standard deviation for their mass is 2 milligrams. We want to get a 95% confidence interval for the mass of a single microchip produced here. So we randomly sample 100 microchips. The sample average mass turns out to be 1972 milligrams. They found this by placing them all on a scale at once and finding a mass of 197.2 grams, and then dividing by 100. You don't think they would actually weigh each one individually, do you? That would be super annoying. Required:
Find a 95% confidence interval for the mass of a microchip produced at this factory.

The 95% confidence interval for the mass of a microchip produced at this factory is between 1971.608 milligrams and 1972.392 milligrams.

Step-by-step explanation:

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

Now, we have to find z in the Z-table as such z has a p-value of .

That is z with a pvalue of , so Z = 1.96.

Now, find the margin of error M as such

In which is the standard deviation of the population and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 1972 - 0.392 = 1971.608 milligrams

The upper end of the interval is the sample mean added to M. So it is 1972 + 0.392 = 1972.392 milligrams

The 95% confidence interval for the mass of a microchip produced at this factory is between 1971.608 milligrams and 1972.392 milligrams.

b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation:

for future students the answer is b

hope i

-lavira: )