data; [7 4 3 6 5 5 6 7 6 6 4 6 3 5 5 4 4 6 7 6 0 7 6 8 5 6 6 5 6 5] YOU HAVE ONLY 30 MINUTES !!!! Question 2) Sampling distribution (17%) ADA university reported mean score for the GMAT test on writi

data; [7 4 3 6 5 5 6 7 6 6 4 6 3 5 5 4 4 6 7 6 0 7 6 8 5 6 6 5 6 5]

YOU HAVE ONLY 30 MINUTES !!!!

Question 2) Sampling distribution (17%) 

ADA university reported mean score for the GMAT test on writing is 494. Assume that the population standard deviation on each part of the test is standard deviation is 100. Sample size is also 100. 

a)     What is the standard error of the sample mean for a sample of 100 test takers? (5%)

b)    What is the probability a sample of 100 test takers will provide a sample mean test score within 16 points of the population mean of 494 on the Writing part of the test?  (7%)

c)     What would be the effect of taking a larger sample on the probabilities? Explain. (6%)

In all answers show your calculations (Except variance calculation in question 1. But full points will be given to the correct answer). 

 I need well explained answer !!!!