Question
In: Math
A tire company produced a batch of 5 comma 300 tires that includes exactly 260 that...
A tire company produced a batch of 5 comma 300 tires that includes exactly 260 that are defective. a. If 4 tires are randomly selected for installation on a car, what is the probability that they are all good? b. If 100 tires are randomly selected for shipment to an outlet, what is the probability that they are all good? Should this outlet plan to deal with defective tires returned by consumers?
Solutions
Expert Solution
From the information, the number of tires in the experiment be
. The tires for installation on a car
are assumed to be independent of each other.
The possible outcomes are the tires are “defective” and “good”. Let X be the number of tires are defective. Here, the requirements of a binomial experiment are satisfied. Hence, the binomial distribution is appropriate.
From the given information
, and 
.
The probability that they are all good when 4 tires are randomly selected for installation on a car is obtained as given below:
P(all are good) = P(no defective)
= P(X=0)
= 
The probability that all the tires are good is 0.818.
From the information, the sample size is 100 tires with probability
of 0.0426. The probability that tires are all good is obtained by
substituting corresponding values in the 
.
From the given information
, and .
The probability that tires are all good when 100 tires are
randomly selected for shipment to an outlet is obtained as given
below:
P(all are good) = P(no defective)
= P(X=0)
=
The probability that tires are all good when 100 tires are randomly selected for shipment to an outlet is 0.0066.
The probability that all the tires are good is 0.8402.
The probability that tires are all good when 100 tires are randomly
selected for shipment to an outlet is 0.0066.
Yes, because there is a very small possibility that all 100 tires are good.
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Cash
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52,000
Accounts Receivable
35,000
Raw Materials Inventory 1,900
Finished Goods Inventory 2,400
________
Total Current Assets
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Property, Plant, and Equipment:
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________...
The Gessing Tire Company manufactures racing tires for bicycles. Gessing sells tires for $85 each. Gessing...
The
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Gessing sells tires for $85 each. Gessing is planning for the next
year by developing a master budget by quarters. Gessing’s balance
sheet for December 31, 2018, follows:
Gessing Tire Company
Balance sheet
December 31, 2018
Current
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Cash
$
52,000
Accounts Receivable
35,000
Raw Materials Inventory 1,900
Finished Goods Inventory 2,400
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$
91,300
Property, Plant, and Equipment:
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92,000
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The Grilton Tire Company manufactures racing tires for bicycles. Grilton sells tires for $50 each. Grilton...
The Grilton Tire Company manufactures racing tires for bicycles.
Grilton sells tires for $50 each. Grilton is planning for next year
by developing a master budget by quarters. Grilton’s balance sheet
for December 31, 2016 follows:
GRILTON TIRE COMPANY
Balance Sheet
December 31, 2016
Assets
Current Assets:
Cash
$
39,000
Accounts
Receivable
40,000
Raw Materials
Inventory
2,400
Finished Goods
Inventory
8,700
Total Current
Assets
$
90,100
Property, Plant and Equipment:
Equipment
177,000
Less:...
The Grilton Tire Company manufactures racing tires for bicycles. Grilton sells tires for $50 each. Grilton...
The Grilton Tire Company manufactures racing tires for bicycles.
Grilton sells tires for $50 each. Grilton is planning for next year
by developing a master budget by quarters. Grilton’s balance sheet
for December 31, 2017 follows:
GRILTON TIRE COMPANY
Balance Sheet
December 31, 2017
Assets
Current Assets:
Cash
$
39,000
Accounts
Receivable
40,000
Raw Materials
Inventory
2,400
Finished Goods
Inventory
8,700
Total Current
Assets
$ 90,100
Property, Plant and Equipment:
Equipment
177,000
Less:...
The Grilton Tire Company manufactures racing tires for bicycles. Grilton sells tires for $50 each. Grilton...
The Grilton Tire Company manufactures racing tires for bicycles.
Grilton sells tires for $50 each. Grilton is planning for next year
by developing a master budget by quarters. Grilton’s balance sheet
for December 31, 2016 follows:
GRILTON TIRE COMPANY
Balance Sheet
December 31, 2016
Assets
Current Assets:
Cash
$
39,000
Accounts
Receivable
40,000
Raw Materials
Inventory
2,400
Finished Goods
Inventory
8,700
Total Current
Assets
$
90,100
Property, Plant and Equipment:
Equipment
177,000
Less:...
The Grilton Tire Company manufactures racing tires for bicycles. Grilton sells tires for $50 each. Grilton...
The Grilton Tire Company manufactures racing tires for bicycles.
Grilton sells tires for $50 each. Grilton is planning for next year
by developing a master budget by quarters. Grilton’s balance sheet
for December 31, 2016 follows:
GRILTON TIRE COMPANY
Balance Sheet
December 31, 2016
Assets
Current Assets:
Cash $ 39,000
Accounts
Receivable 40,000
Raw Materials
Inventory 2,400
Finished Goods
Inventory 8,700
Total Current
Assets $ 90,100
Property, Plant and Equipment:
Equipment 177,000
Less: Accumulated
Depreciation (42,000) 135,000
Total
Assets $225,100
Liabilities
Current Liabilities:
Accounts
Payable $ 8,000
Stockholder’s Equity
Common Stock, no
par $...
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by developing a master budget by quarters. Grilton’s balance sheet
for December 31, 2017 follows:
GRILTON TIRE COMPANY
Balance Sheet
December 31, 2017
Assets
Current Assets:
Cash
$
39,000
Accounts
Receivable
40,000
Raw Materials
Inventory
2,400
Finished Goods
Inventory
8,700
Total Current
Assets
$ 90,100
Property, Plant and Equipment:
Equipment
177,000
Less:...
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