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My name is Ann [436]
3 years ago
10

A medical facility does MRIs. Occasionally, the test yield inconclusive results and have to be repeated. Using the following sam

ple data and n = 100, determine the UCL (to three decimals) for a two-sigma control chart.
Sample 1 2 3 4 5 6 7 8 9 10
Number of Retests 4 11 6 10 4 6 1 6 9 11
a) 0.118.
b) 0.068.
c) 0.144.
d) 0.129.
Business
1 answer:
kupik [55]3 years ago
5 0

Answer:

a) 0.118.

Explanation:

The computation of the UCL is shown below:

Given that

N = 100

<u>Sample    Sample size      Number of retests       fraction defective </u>

1                      100                     4                                0.04

2                     100                      11                               0.11

3                     100                      6                               0.06

4                     100                      10                              0.1

5                     100                     4                                0.04

6                     100                      6                              0.04

7                     100                      1                                0.01

8                     100                      6                               0.06

9                     100                      9                              0.09

10                   100                      11                               0.11

Total              1,000                   68

Now p is

= 68 ÷ 1000

= 0.068

Now the standard deviation is

= √p(1 - p) ÷ √n

= √0.068 × (1 - 0.068) ÷ √100

= 0.025

Now the UCL is

= p + z × standard deviation

= 0.068 + 2 × 0.025

= 0.118

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  2. total period costs incurred to make 27,500 units = $15.10 x 27,500 = $415,250
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Explanation:

                                                       Average Cost per Unit

  • Direct materials                                   $8.90
  • Direct labor                                           $5.90
  • Variable manufacturing overhead   $3.40
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  • Fixed administrative expense           $4.40
  • Sales commissions                           $2.90
  • Variable administrative expense           $2.40

Product costs include direct labor, direct materials, production supplies, and factory overhead. Product costs per unit = $8.90 + $5.90 + $3.40 + $6.90 = $25.10

Period costs include selling and administrative expenses. Period costs per unit = $5.40 + $4.40 + $2.90 + $2.40 = $15.10

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