Question
In: Statistics and Probability
A warehouse receives orders for a particular product on a regular basis. When an order is...
A warehouse receives orders for a particular product on a regular basis. When an order is placed, customers can order 3, 4, 5, ..., 21 units of the product. Historical data suggest that the size of any given order is equally likely to be of any of these sizes. Let X denote the size of an order.
Find the probability that a customer orders at least five units.
Solutions
Expert Solution
Historical data suggest that the size of any given order is equally likely to be of any of these sizes.
Then, X will follow discrete uniform distribution with range (3, 21). The PMF of X is,
P(X = k) = 1/(21-3 + 1) = 1/19 for k = 3,4, ..., 21
Probability that a customer orders at least five units = P(X
5) = 1 - P(X < 5)
= 1 - P(X 
4)
= 1 - [P(X = 3) + P(X = 4)]
= 1 - [1/19 + 1/19]
= 1 - 2/19
= 17/19
orchestra answered 2 years agoRelated Solutions
A warehouse receives orders for a particular product on a regular basis. When an order is...
A warehouse receives orders for a particular product on a
regular basis. When an order is placed, customers can order 3, 4,
5, ..., 21 units of the product. Historical data suggest that the
size of any given order is equally likely to be of any of these
sizes. Let X denote the size of an order.
Find the probability that a customer orders exactly five
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Osage, Inc., manufactures and sells lamps. The company produces only when it receives orders and, therefore,...
Osage, Inc., manufactures and sells lamps. The company produces
only when it receives orders and, therefore, has no inventories.
The following information is available for the current month:
Actual (based on actual orders for 452,000 units) Master Budget
(based on budgeted orders for 484,000 units)
Sales revenue $ 4,970,000 $ 4,840,000
Less Variable costs Materials 1,450,000 1,452,000
Direct labor 278,000 338,800
Variable overhead 674,600 629,200
Variable marketing and administrative 472,000 484,000
Total variable costs $ 2,874,600 $ 2,904,000
Contribution margin...
Osage, Inc., manufactures and sells lamps. The company produces only when it receives orders and, therefore,...
Osage, Inc., manufactures and sells lamps. The company produces
only when it receives orders and, therefore, has no inventories.
The following information is available for the current month:
Actual (based on actual orders for 460,000
units)
Master Budget (based on budgeted orders for 500,000
units)
Sales revenue
$
4,978,000
$
5,000,000
Less
Variable costs
Materials
1,490,000
1,500,000
Direct labor
286,000
350,000
Variable overhead
675,400
650,000
Variable marketing and administrative
488,000
500,000
Total variable costs
$
2,939,400
$
3,000,000
Contribution...
Osage, Inc., manufactures and sells lamps. The company produces only when it receives orders and, therefore,...
Osage, Inc., manufactures and sells lamps. The company produces
only when it receives orders and, therefore, has no inventories.
The following information is available for the current
month:
Actual (based on actual orders for 450,000
units)
Master Budget (based on budgeted orders for 480,000
units)
Sales revenue
$
4,494,000
$
4,320,000
Less
Variable costs
Materials
1,536,000
1,536,000
Direct labor
224,000
288,000
Variable overhead
627,300
576,000
Variable marketing and administrative
372,000
384,000
Total variable costs
$
2,759,300
$
2,784,000
Contribution margin...
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Osage, Inc., manufactures and sells lamps. The company produces
only when it receives orders and, therefore, has no inventories.
The following information is available for the current month:
Actual (based on actual orders for 450,000 units) Master Budget
(based on budgeted orders for 480,000 units) Sales revenue $
4,968,000 $ 4,800,000 Less Variable costs Materials 1,440,000
1,440,000 Direct labor 276,000 336,000 Variable overhead 674,400
624,000 Variable marketing and administrative 468,000 480,000 Total
variable costs $ 2,858,400 $ 2,880,000 Contribution margin...
Osage, Inc., manufactures and sells lamps. The company produces only when it receives orders and, therefore,...
Osage, Inc., manufactures and sells lamps. The company produces
only when it receives orders and, therefore, has no inventories.
The following information is available for the current month:
Actual (based on actual orders for 458,000
units)
Master Budget (based on budgeted orders for 496,000
units)
Sales revenue
$
4,976,000
$
4,960,000
Less
Variable costs
Materials
1,480,000
1,488,000
Direct labor
284,000
347,200
Variable overhead
675,200
644,800
Variable marketing and administrative
484,000
496,000
Total variable costs
$
2,923,200
$
2,976,000
Contribution...
Osage, Inc., manufactures and sells lamps. The company produces only when it receives orders and, therefore,...
Osage, Inc., manufactures and sells lamps. The company produces
only when it receives orders and, therefore, has no inventories.
The following information is available for the current month:
Actual (based on actual orders for 463,000
units)
Master Budget (based on budgeted orders for 506,000
units)
Sales revenue
$
4,981,000
$
5,060,000
Less
Variable costs
Materials
1,505,000
1,518,000
Direct labor
289,000
354,200
Variable overhead
675,700
657,800
Variable marketing and administrative
494,000
506,000
Total variable costs
$
2,963,700
$
3,036,000
Contribution...
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