Question

In: Statistics and Probability

The maintenance department of a building must replace 8 defective lighting tubes. This service has 40...

The maintenance department of a building must replace 8 defective lighting tubes. This service has 40 tubes in stock with 5 broken tubes. The person who has to replace the tubes decides to choose 10 at random from the stock. What is the probability that the ten tubes are enough to replace the 8 that are defective?

Answer: 0.910712332

Solutions

Expert Solution

Non-defective tubes = 35

Defective tubes= 5

Total tubes = 40

Number of tubes selected = 10

Let X = Number of Non-defectives:

To find P(X8):

Case1: X = 8

Number of ways of selecting 10 tubes from 40 tubes = 40C10 = 8.47660528 X 108

Number of ways of selecting 8 non-defectives from 35 non-defectives = 35C8 = 2.353582 X 107

Number of ways of selecting 2 defectives from 5 defectives = 5C2 = 10

So,

P(X = 8) = (2.353582 X 107 X 10/ 8.47660528 X 108 )

            = 0.2776561987                                         (1)

Case 2: X = 9

Number of ways of selecting 10 tubes from 40 tubes = 40C10 = 8.47660528 X 108

Number of ways of selecting 9 non-defectives from 35 non-defectives = 35C9 = 7.060746 X 107

Number of ways of selecting 1 defectives from 5 defectives = 5C21 = 5

So,

P(X = 9) = ( 7.060746 X 107 X 5/ 8.47660528 X 108 )

            = 0.416484298                                       (2)

Case 3: X = 10

Number of ways of selecting 10 tubes from 40 tubes = 40C10 = 8.47660528 X 108

Number of ways of selecting 10 non-defectives from 35 non-defectives = 35C10 = 1.83579396 X 108

So,

P(X = 10) = ( 1.83579396X 108 / 8.47660528 X 108 )

            = 0.21657183                                               (3)

Adding the probability values of P(X = 8) ,P(X = 9) and P(X = 10), given by (1), , (2) & (3), we get the required reslt as follows:
P(X8)=0.910712332

So,

Answer is:

0.21657183         

orchestra answered 1 year ago
Next > < Previous

Related Solutions

Warren Ltd. has two production departments, Building A and Building B, and two service departments, Maintenance...
Warren Ltd. has two production departments, Building A and Building B, and two service departments, Maintenance and Cafeteria. Direct costs for each department and the proportion of service costs used by the various departments for the month of June follow: Proportion of Services Used by    Department Direct Costs Maintenance Cafeteria Building A Building B   Building A $ 480,000   Building B 327,000   Maintenance 182,000 — 0.1 0.7 0.2   Cafeteria 178,000 0.7 — 0.2 0.1 Required: (a) Use the step method...
Mushed’s String Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $320,000 are...
Mushed’s String Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $320,000 are allocated on the basis of budgeted maintenance-hours. Personnel Department costs of $80,000 are allocated based on the number of employees. The costs of operating departments A and B are $160,000 and $240,000, respectively. Data on budgeted maintenance-hours and number of employees are as follows: Support Departments Production Departments Maintenance Personnel A B Budgeted costs $320,000 $80,000 $160,000 $240,000 Budgeted maintenance-hours NA 200 240 160...
Hanung Corp has two service departments, Maintenance and Personnel. Maintenance Department costs of $300,000 are allocated...
Hanung Corp has two service departments, Maintenance and Personnel. Maintenance Department costs of $300,000 are allocated on the basis of budgeted maintenance-hours. Personnel Department costs of $100,000 are allocated based on the number of employees. The costs of operating departments A and B are $160,000 and $240,000, respectively. Data on budgeted maintenance-hours and number of employees are as follows: Support Departments Production Departments Maintenance Department Personnel Department A B Budgeted costs $300,000 $100,000 $160,000 $240,000 Budgeted maintenance-hours NA 800 1,200...
Jake's Battery Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $160,000 are...
Jake's Battery Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $160,000 are allocated on the basis of budgeted maintenance-hours. Personnel Department costs of $40,000 are allocated based on the number of employees. The costs of operating departments A and B are $80,000 and $120,000, respectively. Data on budgeted maintenance-hours and number of employees are as follows: Support Departments Production Departments Maintenance Department Personnel Department A B Budgeted costs $160,000 $40,000 $80,000 $120,000 Budgeted maintenance-hours NA 400...
Jake's Battery Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $300,000 are...
Jake's Battery Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $300,000 are allocated on the basis of budgeted machine-hours. Personnel Department costs of $100,000 are allocated based on the number of employees. The costs of operating departments A and B are $160,000 and $240,000, respectively. Data on budgeted maintenance-hours and number of employees are as follows: Support Departments Production Departments Maintenance Department Personnel Department A B Budgeted costs $300,000 $100,000 $160,000 $240,000 Budgeted maintenance-hours NA 800...
Bolton Corp has two service departments, Maintenance and Personnel. Maintenance Department costs of $300,000 are allocated...
Bolton Corp has two service departments, Maintenance and Personnel. Maintenance Department costs of $300,000 are allocated on the basis of budgeted maintenance-hours. Personnel Department costs of $100,000 are allocated based on the number of employees. The costs of operating departments A and B are $160,000 and $240,000, respectively. Data on budgeted maintenance-hours and number of employees are as follows: Support Departments Production Departments Maintenance Department Personnel Department A B Budgeted costs $300,000 $100,000 $160,000 $240,000 Budgeted maintenance-hours NA 800 1,200...
Steven's Battery Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $320,000 are...
Steven's Battery Company has two service departments, Maintenance and Personnel. Maintenance Department costs of $320,000 are allocated on the basis of budgeted maintenance-hours. Personnel Department costs of $80,000 are allocated based on the number of employees. The costs of operating departments A and B are $160,000 and $240,000, respectively. Data on budgeted maintenance-hours and number of employees are as follows: Support Departments Production Department Maint Department Personnel Department A B Budgeted Costs $320,000 $80,000 $160,000 $240,000 Budgeted Maintenance hours NA...
Question 4: Service department cost allocation Inns Battery Company has two service departments: Maintenance and Personnel....
Question 4: Service department cost allocation Inns Battery Company has two service departments: Maintenance and Personnel. Maintenance Department costs are allocated on the basis of budgeted maintenance-hours. Personnel Department costs are allocated based on the number of employees. Data on budgeted maintenance-hours and number of employees are as follows: Support Departments Production Departments Maintenance Department Personnel Department A B Budgeted costs $180,000 $30,000 $80,000 $120,000 Budgeted maintenance-hours n/a 240 720 240 Number of employees 20 n/a 60 120 Required: 4a....
The maintenance of arms has been crucial in state building and maintenance since the formation of...
The maintenance of arms has been crucial in state building and maintenance since the formation of nations. There has been a gradual shift over time in the primary function of arms from offensive to defensive. However, the spending of arms is at an all time high even though we are in a period of (relative) peace. This is likely to originate from the influence the Military Industrial Complex has on national and international politics. (Comment the paragraph in 100 words)
. A 40-unit apartment building is placed into service on August 15, 2013 at a cost...
. A 40-unit apartment building is placed into service on August 15, 2013 at a cost of $1,000,000. The apartments will rent for $850-$1200 per month. The owners sell the apartment building on June 1, 2017 for $850,000. a) Find the depreciation deduction and unrecovered investment (Book Value) for each tax year involved. b) What is the difference between the Book Value and the sales price in 2017? c) What taxes will the owners owe, (or what tax credit will...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT