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wariber [46]
2 years ago
14

An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates

that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months. On the basis of this information, determine the percentage of scanners that can be expected to fail in the following time periods:
a. Before 38 months of service
b. Between 40 and 45 months of service
c. Within ± 2 months of the mean life
Business
1 answer:
goldenfox [79]2 years ago
5 0

Answer:

a) 22.663%

b) 44%

c) 38.3%

Explanation:

An office manager has received a report from a consultant that includes a section on equipment replacement. The report indicates that scanners have a service life that is normally distributed with a mean of 41 months and a standard deviation of 4 months. On the basis of this information, determine the percentage of scanners that can be expected to fail in the following time periods:

We solve the above question using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean = 41 months

σ is the population standard deviation = 4 months

a. Before 38 months of service

Before in z score score means less than 38 months

Hence,

z = 38 - 41/4

z = -0.75

Probability value from Z-Table:

P(x<38) = 0.22663

Converting to percentage = 0.22663 × 100

= 22.663%

b. Between 40 and 45 months of service

For x = 40 months

z = 40 - 41/4

z = -0.2

Probability value from Z-Table:

P(x = 40) = 0.40129

For x = 45

z = 45 - 41/4

z = 1

Probability value from Z-Table:

P(x = 45) = 0.84134

Between 40 and 45 months of service

= 0.84134 - 0.40129

= 0.44005

Converting to Percentage

= 0.44005 × 100

= 44.005%

= 44%

c. Within ± 2 months of the mean life

+ 2 months = 41 months + 2 months

= 43 months

- 2 months = 41 months - 2 months

= 39 months

For x = 43

z = 43 - 41 /4

z = 0.5

P-value from Z-Table:

P(x = 43) = 0.69146

For x = 39

z = 39 - 41/4

z = -2/4

z = -0.5

Probability value from Z-Table:

P(x = 39) = 0.30854

Within ± 2 months of the mean life

= 0.69146 - 0.30854

= 0.38292

= 38.3%

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<u>Foster Manufacturing </u>

<u>Journal Entries</u>

<u>Sr. No                       Particulars                       Debit           Credit</u>

1                    Work in Process Job No. 221        1200

                    Work in Process Job No. 222      1700

                   Work in Process Job No. 223       2400

                    Work in Process Job No. 224      2600

         Factory Overhead  Indirect Materials      600

                              Materials Inventory                                  8500

Materials Requisitioned to specific jobs work in process inventory.

2. Direct Labor    Work in Process Job No. 221        1600

     Direct Labor  Work in Process Job No. 222      2200

  Direct Labor    Work in Process Job No. 223       2900

    Direct Labor Work in Process Job No. 224      2800

                                                   Indirect Labor      400

                                      Payroll                                               9500

                                         Factory OverheadControl               400

Direct Labor used for specific jobs.

3.          Work in Process Job No. 221              1120

                    Work in Process Job No. 222      1540

                   Work in Process Job No. 223       2030

                    Work in Process Job No. 224      1960  

                         Manufacturing Overheads                            6930

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         Work in Process Job No. 221 MOH                          1540

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