The line width of a tool used for semiconductor manufacturing is assumed to be normally distributed with a mean of 0.5micrometer and a standard deviation of 0.05
micrometer.

(a) What is the probability that a line width is greater than 0.62 micrometer?
(b) What is the probability that a line width is between 0.47and 0.63 micrometer?
(c) The line width of 90%of samples is below what value?

center (1,3) with radius 6

step-by-step explanation:

we must complete the square to find the center and radius of the circle.

first make sure the x and y squared terms have 1 as their coefficients. we also make sure x and y terms together.

we now create space between the x and y terms with parenthesis.

we complete the square by taking the middle terms -2x and the -6y - divide each and square them.

we add the squares to both sides.

simplify.

and write the quadratics in factored form.

the center is (h,k) or (1,3). the radius is the square root of 36 which is 6.

it is ok do not worry about it my dude. have a good one