Recently. there has been a lot of discussion in the press about students taking a 'gap year' between high school and post-secondary education. Faculty members at a locaI university were wondering what effect this has on the age of students at their institution. They took a random sample of 50 students, and asked them their age. The mean age was 21.68 years. with a standard deviation of 3.873 years. In the context of the problem. are the assumptions and conditions met? For each assumption. name the condition and clearly explain if it is met or not. \fNormal Population Assumption: we do not know the shape of the population distribution of age but it is unlikely to be normal [if there are mature students, it would be right-skewed otherwise it would be uniform], so we need to consider the sample size. Is the sample size assumption met? 1 A * B ICalculate a 95% condence interval. Show your work by lling in the appropriate values below. Round your nal answer to 3 places after the decimal. Degrees of Freedom: Which of the following is the correct interpretation of the condence interval? 0 a. Since the assumptions are met. we are 95% condent that the average age will be between 20.6 and 22.8 years. for the population of all university students. 0 b. Since the assumptions are met. we are 95% condent that the average age will be between 20.6 and 22.8 years. for the population of all students at this university. 0 c. Since the assumptions are met. we are 95% condent that the average age will be between 20.6 and 22.8 years. for the population of the 50 students at this university. 0 d. Since the assumptions are met. we are 95% condent that the for the population of all students at this university. they are between 20.6 and 22.8 years old