The diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long. Any washers that do not meet this requirement must be discarded. What percentage of washers will the factory have to discard

32%

Step-by-step explanation:

Let x be the mean of the values and σ their standard deviation.

Since the minimum value of the diameter of the washers is 1.53 mm, then

x - σ = 1.53 mm  (1)

Also, the maximum value of the diameter of the washers is 1.65 mm, then

x + σ = 1.65 mm  (2)

Adding (1) and (2), we have

x - σ = 1.53 mm

+

x + σ = 1.65 mm  

2x = 3.18

x = 3.18/2

x = 1.59 mm

Subtracting (1) and (2), we have

x - σ = 1.53 mm

-

x + σ = 1.65 mm  

-2σ = -0.12

σ = -0.12/-2

σ = 0.06 mm

Since the diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long, and x - σ = 1.53 mm to x + σ = 1.65 mm are the required values, 68% of the washers lie in this range. The other values lie outside this range. The amount that the factory would have to discard is 100% - 68% = 32%

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x