A company manufactures a part for which there is a desired weight. There is a tolerance of N%, meaning that the range between minus and plus N% of the desired weight is acceptable. The tolerance is 1.5% for this particular part.

Given the following vector $ W $, where the desired weight is 97:

\[ [97, 98.2, 95.5, 97.2, 96.2, 100, 99.9, 99.8, 96.1] \]

1. Determine the tolerance range for 97 and place the values in variables `low_97` and `high_97`.
2. Determine if each of the values in vector $ W $ is within the tolerance or not. Create a logical vector called `within` with 0s and 1s as output.
3. Create an output matrix `mat` where the first row is $ W $ and the second row indicates whether each value in $ W $ is within the tolerance.

To calculate the tolerance for a desired weight, we use the formula desired weight +/- (desired weight * tolerance). We then compare each value in the given vector to the tolerance limits to determine if it is within the tolerance. The result is a matrix showing the values and their within tolerance status.

Explanation:

The tolerance for a desired weight of 97 with a tolerance of 1.5% is calculated as follows:

Low_97 = 97 - (97 * 0.015)

High_97 = 97 + (97 * 0.015)

Low_97 = 97 - 1.455

High_97 = 97 + 1.455

Low_97 = 95.545

High_97 = 98.545

To determine if each value in the vector W is within the tolerance, we compare each value to the low and high limits:

If a value is greater than or equal to the low limit and less than or equal to the high limit, it is within the tolerance and marked as 1 in the within vector.

If a value is outside the tolerance range, it is not within the tolerance and marked as 0 in the within vector.

The output matrix mat is a 2x9 matrix with the first row being the vector W and the second row being the within vector.

Chimara Chimara · Answer 2 · 2023-07-22T21:09:31-04:00

Answer:

Step-by-step explanation:

(A) Determine what the tolerance is for the desired weight 97

The tolerance N% is equal to 1.5% of 97

1.5/100 × 97 = 1.455

Lower limit = 97 - 1.455 = 95.545

Upper limit = 97 + 1.455 = 98.455

(B) Place the vector values into two groups;

- Variables lower than 97

95.5, -97.2, 96.2, 96.1

- Variables higher than 97

98.2, 100, 99.9, 99.8

(C) Determine if each of the values is within the tolerance bracket or not

1. Value 97 is within the tolerance. As a matter of fact, it is the desired weight.

2. Value 98.2 is within the tolerance

3. Value 95.5 is within the tolerance

4. Value -97.2 is far below the tolerance bracket or lower limit

5. Value 96.2 is within the tolerance

6. Value 100 is outside the tolerance

7. Value 99.9 is outside the tolerance

8. Value 99.8 is outside the tolerance

9. Value 96.1 is within the tolerance