Question

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0963 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 296 independent returns from this year, what is the probability that between 29 and 32 (inclusively) will be fraudulent or will contain errors that are purposely made to cheat the IRS?

Question 6 options:

1)0.7228
2)0.2772
3)1.3751
4) -0.0194
5) 0.1366

Answer 1

B.) 0.2772

Explanation:

By using binomial distribution for r=29,30,31,32.

296C29*(0.0963^29)(1-0.0963)^267+

296C30*(0.0963^30)(1-0.0963)^266+

296C31*(0.0963^31)(1-0.0963)^265+

296C32*(0.0963^32)(1-0.0963)^264

.

(1.2739*10^40)(3.3509*10^-30)(1.81335*10^-12)+

(1.13378*10^41)(6.475118*10^-43)+

(9.7285*10^41)(6.9*10^-44)+

(8.056449*10^42)(7.35278*10^-45)

=0.277174