Question

Question 5 of 26 fi Time Remaining: 00:34:35 6 Points A random sample of 20 marks from an A scores in STAT 111 is listed as: 25. 26. 13. 23. 23. 25. 17. 22. 17. 19. 12. 26. 30. 30. 18. 14. 12. 26. 17. 18. The mean and the standard deviation are 20.65 and 5.71 respectively. The lecturer decided to add 5 marks to each student's mark Calculate the sample mean and sample standard deviation of the new marks O A 101.75.25.71 OB. 25.65, 10.71 OC 25.65.5.71 OD 20.65.5.71 O E. 20.65, 10.71​

Answer 1

option (C): 25.65, 5.71.

Explanation:

To find the new sample mean and standard deviation after adding 5 marks to each student's mark, we can use the following formulas:

New sample mean = Old sample mean + 5

New sample standard deviation = Old sample standard deviation

Using the given values, the old sample mean is 20.65, so the new sample mean is:

New sample mean = 20.65 + 5 = 25.65

To find the new sample standard deviation, we simply use the given value of 5.71:

New sample standard deviation = 5.71

Therefore, the answer is option (C): 25.65, 5.71.

Answer 2

To calculate the new sample mean and standard deviation after adding 5 to each mark, we simply add 5 to each mark and then recalculate the mean and standard deviation:

Original marks: 25, 26, 13, 23, 23, 25, 17, 22, 17, 19, 12, 26, 30, 30, 18, 14, 12, 26, 17, 18

New marks: 30, 31, 18, 28, 28, 30, 22, 27, 22, 24, 17, 31, 35, 35, 23, 19, 17, 31, 22, 23

New sample mean = (30 + 31 + 18 + 28 + 28 + 30 + 22 + 27 + 22 + 24 + 17 + 31 + 35 + 35 + 23 + 19 + 17 + 31 + 22 + 23) / 20

= 25.65

New sample standard deviation = sqrt[((30-25.65)^2 + (31-25.65)^2 + (18-25.65)^2 + ... + (23-25.65)^2)/19]

= 10.71

Therefore, the answer is option B: 25.65, 10.71.