The tax reform act of 1986 contains a change in accounting methods with regard t
ID: 3201913 • Letter: T
Question
The tax reform act of 1986 contains a change in accounting methods with regard to inventory capitalization. The law states that inventory costs, such as storage a warehousing of inventory--Which had previously been considered expense--are to be capitalized, thus inceasing a corporation's taxable income. In a survey by the National Association of Accountants, 60% of the corporate accountants who responded did not know what effect this law would have on their corporate tax liability. Suppose that this percentage applies to all corporate accountants, and n=19 corporate accountants are questioned regarding the new tax law.
a) Find the probability that at least 15 of the 19 do not know what effect the law will have on their corporate tax liabilities.
b) Find the probability that no more than 10 do not know what effect the law will have
c) If only 10 of the 19 corporate accountants did not know what effect this law would have on their corporate liabilities, what would you conclude regarding the accuracy of the 60% figure given in this survey?
Explanation / Answer
Result:
The tax reform act of 1986 contains a change in accounting methods with regard to inventory capitalization. The law states that inventory costs, such as storage a warehousing of inventory--Which had previously been considered expense--are to be capitalized, thus inceasing a corporation's taxable income. In a survey by the National Association of Accountants, 60% of the corporate accountants who responded did not know what effect this law would have on their corporate tax liability. Suppose that this percentage applies to all corporate accountants, and n=19 corporate accountants are questioned regarding the new tax law.
P( x 15) =0.0696
b) Find the probability that no more than 10 do not know what effect the law will have
P( x10) =0.3325
Expectation = np = 11.4
Variance = np(1 - p) = 4.56
Standard deviation = 2.1354
The value 10 is within 2 standard deviation of the mean value of 11.4.
There is no concern about the accuracy of the 60% figure given in this survey.
n=19
p=0.6
P(X=x) = (nCx) px (1-p)n-x
Binomial Probabilities Table
X
P(X)
P(<=X)
P(<X)
P(>X)
P(>=X)
0
0.0000
0.0000
0.0000
1.0000
1.0000
1
0.0000
0.0000
0.0000
1.0000
1.0000
2
0.0000
0.0000
0.0000
1.0000
1.0000
3
0.0001
0.0001
0.0000
0.9999
1.0000
4
0.0005
0.0006
0.0001
0.9994
0.9999
5
0.0024
0.0031
0.0006
0.9969
0.9994
6
0.0085
0.0116
0.0031
0.9884
0.9969
7
0.0237
0.0352
0.0116
0.9648
0.9884
8
0.0532
0.0885
0.0352
0.9115
0.9648
9
0.0976
0.1861
0.0885
0.8139
0.9115
10
0.1464
0.3325
0.1861
0.6675
0.8139
11
0.1797
0.5122
0.3325
0.4878
0.6675
12
0.1797
0.6919
0.5122
0.3081
0.4878
13
0.1451
0.8371
0.6919
0.1629
0.3081
14
0.0933
0.9304
0.8371
0.0696
0.1629
15
0.0467
0.9770
0.9304
0.0230
0.0696
16
0.0175
0.9945
0.9770
0.0055
0.0230
17
0.0046
0.9992
0.9945
0.0008
0.0055
18
0.0008
0.9999
0.9992
0.0001
0.0008
19
0.0001
1.0000
0.9999
0.0000
0.0001
Binomial Probabilities Table
X
P(X)
P(<=X)
P(<X)
P(>X)
P(>=X)
0
0.0000
0.0000
0.0000
1.0000
1.0000
1
0.0000
0.0000
0.0000
1.0000
1.0000
2
0.0000
0.0000
0.0000
1.0000
1.0000
3
0.0001
0.0001
0.0000
0.9999
1.0000
4
0.0005
0.0006
0.0001
0.9994
0.9999
5
0.0024
0.0031
0.0006
0.9969
0.9994
6
0.0085
0.0116
0.0031
0.9884
0.9969
7
0.0237
0.0352
0.0116
0.9648
0.9884
8
0.0532
0.0885
0.0352
0.9115
0.9648
9
0.0976
0.1861
0.0885
0.8139
0.9115
10
0.1464
0.3325
0.1861
0.6675
0.8139
11
0.1797
0.5122
0.3325
0.4878
0.6675
12
0.1797
0.6919
0.5122
0.3081
0.4878
13
0.1451
0.8371
0.6919
0.1629
0.3081
14
0.0933
0.9304
0.8371
0.0696
0.1629
15
0.0467
0.9770
0.9304
0.0230
0.0696
16
0.0175
0.9945
0.9770
0.0055
0.0230
17
0.0046
0.9992
0.9945
0.0008
0.0055
18
0.0008
0.9999
0.9992
0.0001
0.0008
19
0.0001
1.0000
0.9999
0.0000
0.0001
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