Internal auditors sometimes check random samples of transactions within a database. Suppose that in a particular set of transactions, 2% contain an...

Internal auditors sometimes check random samples of transactions within a database. Suppose that in a particular set of transactions, 2% contain an error of some kind. The auditor takes a random sample of 20 transactions for checking. Let X denote the number of transactions found to be in error in the sample.

(a)       State the probability distribution of X (including the values of all parameters) and find the probability that 2 transactions are found to be in error.   

(b)       If three or more transactions are found to be in error then a larger sample is taken for checking. How often will this happen? (Use the appropriate template).

(c)       What assumption is required for the validity of the above answers?

Data

Sample size100

Probability of success0.2

Statistics

Mean20

Variance16

Standard deviation4

Binomial Probabilities Table

XP(X)Cumulative

00.000000.00000

10.000000.00000

20.000000.00000

30.000000.00000

40.000000.00000

50.000010.00002

60.000060.00008

70.000200.00028

80.000580.00086

90.001480.00233

100.003360.00570

110.006880.01257

120.012750.02533

130.021580.04691

140.033530.08044

150.048060.12851

160.063830.19234

170.078850.27119

180.090900.36209

190.098070.46016

200.099300.55946

210.094570.65403

220.084900.73893

230.071980.81091

240.057730.86865

250.043880.91252

260.031640.94417

270.021680.96585

280.014130.97998

290.008770.98875

300.005190.99394

310.002930.99687

320.001580.99845

330.000810.99926

340.000400.99966

350.000190.99985

360.000090.99994

370.000040.99998

380.000020.99999

390.000011.00000

400.000001.00000

410.000001.00000

420.000001.00000

430.000001.00000

440.000001.00000

450.000001.00000

460.000001.00000

470.000001.00000

480.000001.00000

490.000001.00000

500.000001.00000

510.000001.00000

520.000001.00000

530.000001.00000

540.000001.00000

550.000001.00000

560.000001.00000

570.000001.00000

580.000001.00000

590.000001.00000

600.000001.00000

610.000001.00000

620.000001.00000

630.000001.00000

640.000001.00000

650.000001.00000

660.000001.00000

670.000001.00000

680.000001.00000

690.000001.00000

700.000001.00000

710.000001.00000

720.000001.00000

730.000001.00000

740.000001.00000

750.000001.00000

760.000001.00000

770.000001.00000

780.000001.00000

790.000001.00000

800.000001.00000

810.000001.00000

820.000001.00000

830.000001.00000

840.000001.00000

850.000001.00000

860.000001.00000

870.000001.00000

880.000001.00000

890.000001.00000

900.000001.00000

910.000001.00000

920.000001.00000

930.000001.00000

940.000001.00000

950.000001.00000

960.000001.00000

970.000001.00000

980.000001.00000

990.000001.00000

1000.000001.00000