Question

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0921 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 374 independent returns from this year, what is the probability that at least 36 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Question 4 options:

1)

0.6511

2)

0.0672

3)

0.4161

4)

0.3489

5)

0.0336

Answer 1

n = 374

p = 0.0921

= n * p = 374 * 0.0921 = 34.4

= sqrt(np(1 - p))

   = sqrt(374 * 0.0921 * (1 - 0.0921))

= 5.5922

P(X > 36)

= P((X - )/> (35.5 - )/)

= P(Z > (35.5 - 34.4)/5.5922)

= P(Z > 0.20)

= 1 - P(Z < 0.20)

= 1 - 0.5793

= 0.4207

Option - 3 is correct