Question

an auto transmission manufacturer receives ball bearings from two different suppliers. the ball bearings must have a specified diameter of 16.30 mm with a tolerance of ±0.1 mm. recent shipments from the two suppliers had ball bearings with the following diameters. complete parts (a) through (c).
supplier a: 16.24 16.29 16.32 16.34 16.37 16.42 16.44
supplier b: 16.17 16.22 16.24 16.33 16.37 16.42 16.47
...
c. what percentage of ball bearings from each supplier meet specifications?
find the percentage of ball bearings from supplier a that meet specifications.
71 % (round to the nearest integer as needed.)
find the percentage of ball bearings from supplier b that meet specifications.
□% (round to the nearest integer as needed.)

Explanation:

Step1: Determine Specification Range

The specified diameter is \( 16.30 \pm 0.1 \) mm, so the range is \( 16.30 - 0.1 = 16.20 \) mm to \( 16.30 + 0.1 = 16.40 \) mm.

Step2: Count Valid for Supplier B

Supplier B's diameters: \( 16.17, 16.22, 16.24, 16.33, 16.37, 16.42, 16.47 \).
Check which are between \( 16.20 \) and \( 16.40 \):

• \( 16.22 \): valid
• \( 16.24 \): valid
• \( 16.33 \): valid
• \( 16.37 \): valid
• \( 16.17 \): invalid ( < 16.20)
• \( 16.42 \): invalid ( > 16.40)
• \( 16.47 \): invalid ( > 16.40)

Valid count: \( 4 \).

Step3: Calculate Percentage for B

Total for B: \( 7 \). Percentage = \( \frac{4}{7} \times 100 \approx 57.14 \), rounded to nearest integer is \( 57 \).

Answer:

57