I need help to solve these two questions in R language/program, I need to have a code of the solution and with results?

Question 1:

1.1.If the probability is 0.60 that a person shopping at a certain market will spend at least R25, find the probabilities that among five persons at this market less than four but more than one will spend at least R25.

1.2.Suppose that my consulting business receives an average of 30 phone calls per hour. During a two-hour period, I want to determine the following:

a)The probability that exactly 60 class will be received in the next two hours.

b)The probability that the number of calls received in the next two hours will be fewer than or equal to 60.

c)The probability that from 50 through 100 calls will be received in the next two hours.

1.3. An electrical firm manufacturers lights bulb, which have a lifetime that is Normally Distributed with a mean of 800 hours and standard deviation of 40 hours. Of 100 Bulbs, about how many will have lifetimes between 788 and 834 hours?

1.Question 2:

1.1. An Office manager claims that the mean time required to handle a customer complaint is more than 30 minutes. A sample of 38 complaints shows a sampling mean of 28.7 minutes and standard deviation of 12 minutes. Answer the following:

a) State the hypothesis to test the manager's claim.

b) Find the critical region to test the above hypothesis at the 5% significance level.

C) Calculate the value of the test statistic to test the hypothesis.

d) State the correct conclusion.

1.2. Suppose a sample of 20 students were given a diagnostic test before studying a particular subject and then again after completing the subject. We want to find out if, in general our teaching leads to improvements in students' knowledge/ skills (i.e tests Scores). We want to use the results from our sample of students to draw conclusions about the impact of the subject in general.

a)State the hypothesis

b)Find the critical region to test the above hypothesis at the 5% significance level.

c)Calculate the value of the test statistic to test the hypothesis.

d)State the correct conclusion.

Data2

2104 3 399900

1600 3 329900

2400 3 369000

1416 2 232000

3000 4 539900

1985 4 299900

1534 3 314900

1427 3 198999

1380 3 212000

1494 3 242500

1940 4 239999

2000 3 347000

1890 3 329999

4478 5 699900

1268 3 259900

2300 4 449900

1320 2 299900

1236 3 199900

2609 4 499998

3031 4 599000

1767 3 252900

1888 2 255000

1604 3 242900

1962 4 259900

3890 3 573900

1100 3 249900

1458 3 464500

2526 3 469000

2200 3 475000

2637 3 299900

1839 2 349900

1000 1 169900

2040 4 314900

3137 3 579900

1811 4 285900

1437 3 249900

1239 3 229900

2132 4 345000

4215 4 549000

2162 4 287000

1664 2 368500

2238 3 329900

2567 4 314000

1200 3 299000

852 2 179900

1852 4 299900

1203 3 239500

Data1

6.1101 17.592

5.5277 9.1302

8.5186 13.662

7.0032 11.854

5.8598 6.8233

8.3829 11.886

7.4764 4.3483

8.5781 12

6.4862 6.5987

5.0546 3.8166

5.7107 3.2522

14.164 15.505

5.734 3.1551

8.4084 7.2258

5.6407 0.71618

5.3794 3.5129

6.3654 5.3048

5.1301 0.56077

6.4296 3.6518

7.0708 5.3893

6.1891 3.1386

20.27 21.767

5.4901 4.263

6.3261 5.1875

5.5649 3.0825

18.945 22.638

12.828 13.501

10.957 7.0467

13.176 14.692

22.203 24.147

5.2524 -1.22

6.5894 5.9966

9.2482 12.134

5.8918 1.8495

8.2111 6.5426

7.9334 4.5623

8.0959 4.1164

5.6063 3.3928

12.836 10.117

6.3534 5.4974

5.4069 0.55657

6.8825 3.9115

11.708 5.3854

5.7737 2.4406

7.8247 6.7318

7.0931 1.0463

5.0702 5.1337

5.8014 1.844

11.7 8.0043

5.5416 1.0179

7.5402 6.7504

5.3077 1.8396

7.4239 4.2885

7.6031 4.9981

6.3328 1.4233

6.3589 -1.4211

6.2742 2.4756

5.6397 4.6042

9.3102 3.9624

9.4536 5.4141

8.8254 5.1694

5.1793 -0.74279

21.279 17.929

14.908 12.054

18.959 17.054

7.2182 4.8852

8.2951 5.7442

10.236 7.7754

5.4994 1.0173

20.341 20.992

10.136 6.6799

7.3345 4.0259

6.0062 1.2784

7.2259 3.3411

5.0269 -2.6807

6.5479 0.29678

7.5386 3.8845

5.0365 5.7014

10.274 6.7526

5.1077 2.0576

5.7292 0.47953

5.1884 0.20421

6.3557 0.67861

9.7687 7.5435

6.5159 5.3436

8.5172 4.2415

9.1802 6.7981

6.002 0.92695

5.5204 0.152

5.0594 2.8214

5.7077 1.8451

7.6366 4.2959

5.8707 7.2029

5.3054 1.9869

8.2934 0.14454

13.394 9.0551

5.4369 0.61705

Test_score

Student Subject_Score Subject

1 18 PreSubjectPoints

2 21 PreSubjectPoints

3 16 PreSubjectPoints

4 22 PreSubjectPoints

5 9 PreSubjectPoints

6 24 PreSubjectPoints

7 17 PreSubjectPoints

8 21 PreSubjectPoints

9 23 PreSubjectPoints

10 18 PreSubjectPoints

11 14 PreSubjectPoints

12 16 PreSubjectPoints

13 16 PreSubjectPoints

14 19 PreSubjectPoints

15 18 PreSubjectPoints

16 20 PreSubjectPoints

17 12 PreSubjectPoints

18 22 PreSubjectPoints

19 15 PreSubjectPoints

20 17 PreSubjectPoints

1 22 Post_SubjectScore

2 25 Post_SubjectScore

3 17 Post_SubjectScore

4 24 Post_SubjectScore

5 16 Post_SubjectScore

6 29 Post_SubjectScore

7 20 Post_SubjectScore

8 23 Post_SubjectScore

9 19 Post_SubjectScore

10 20 Post_SubjectScore

11 15 Post_SubjectScore

12 15 Post_SubjectScore

13 18 Post_SubjectScore

14 26 Post_SubjectScore

15 18 Post_SubjectScore

16 24 Post_SubjectScore

17 18 Post_SubjectScore

18 25 Post_SubjectScore

19 19 Post_SubjectScore

20 16 Post_SubjectScore