An engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm, how many of these components should she consider to be 90% sure of knowing the mean will be within ± 0.1 ±0.1 mm?

She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

Step-by-step explanation:

We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.

And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.

As we know that the margin of error is given by the following formula;

The margin of error =    

Here, = standard deviation = 3.6 mm

         n = sample size of components

          = level of significance = 1 - 0.90 = 0.10 or 10%

          = 0.05 or 5%

Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.

So, the margin of error =    

                  0.1 mm        =  

                    = 59.22

                     n = = 3507.0084 ≈ 3507.

Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

the perimeter is increased by a factor of 2