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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

Sagot :

oladayoademosu

Answer:

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%

shristiparmar1221

This question is based on the percentage. Thus, 32%  of washers will the factory have to discard.

Given:

The diameter of the washers are required to be between 1.53 millimeters and 1.65 millimeters long.

We need to determined the percentage of washers will the factory have to discard.

According to question,

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

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

We get,

x = 1.59 mm

Subtracting (1) and (2), we have

 x - σ = 1.53 mm

- x + σ = 1.65 mm  

⇒ -2σ = -0.12

We get,

σ = 0.06 mm

Therefore, 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.

And the other values lie outside this range. The amount that the factory would have to discard is 100% - 68% = 32%.

Thus, 32%  of washers will the factory have to discard.

For more details, prefer this link:

https://brainly.com/question/13703753

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