If a product is comprised of 10 independent parts with each having 3 sigma quality performance (without mean shift), the probability of the entire product to be nondefective is

Given 10 independent part,

No mean shift

This implies that,

The mean is 10

It also means that the variance is 0

And also the standard deviation is 0.

Then, the sigma deviation is

3×0+10=10.

Since none of the data is at such a high point, the manufacturing testing process has not yet reached three-sigma quality levels.

Since we have this let use the special consideration

Three-sigma limits set a range for the process parameter at 0.27% control limits. Three-sigma control limits are used to check data from a process and if it is within statistical control

Therefore,

The 0.27% will give the defective

2.7/100×10=0.027

Then, the none defective is

1-0.027=0.973

Which is 97.3%

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240