I need to justify my answer briefly and show all calculations where needed

6. From a population that is normally distributed with an unknown standard deviation, a "75 elements is selected. For the interval estimation of /, the proper distribution 3 of 3 normal distribution v. - wwutwution c. t distribution with 26 degrees of freedom d. t distribution with 24 degrees of freedom 7. A major department store chain is interested in estimating the mean amount its credit card customers spend on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed providing a sample mean $50.50 and a sample standard deviation of $20. The 95% confidence interval to estimate the actual mean amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution is: a. 41.41 to 59.59 b. 40.38 to 60.62 c. 39.5 to 61.50 d. 39.42 to 61.58 8.. An interval estimate is used to estimate a. the shape of the population's distribution b. the sampling distribution a sample statistic d. a population parameter 9. As the sample size increases, the margin of error a. increases b. decreases C. stays the same d. None of the other answers are correct. 10. A random sample of 36 students at a community college showed an average age of 25 years and a variance of 3.24 years. The 98% confidence interval for the average age of all students at this college is a. 24.301 to 25.699 b. 24.269 to 25.731 24.090 to 25.910 d. 24.131 to 25.869