Asimple random sample of size n is drawn from a population that is normally distributed. the sample mean, x overbar, is found to be 109, and the sample standard deviation, s, is found to be 10. (a) construct a 96% confidence interval about mu if the sample size, n, is 29. (b) construct a 96% confidence interval about mu if the sample size, n, is 25. (c) construct a 90% confidence interval about mu if the sample size, n, is 29. (d) could we have computed the confidence intervals in parts () if the population had not been normally distributed? click the icon to view the table of areas under the t-distribution.

a:  105.2 < µ < 112.8

b:  104.872 < µ < 113.128

c:  105.841 < µ < 112.159

d:  No, because n < 30

Step-by-step explanation:

For a - c, see attached photos for work.  There are 2 formulas to use.  The steps for constructing any confidence interval are the same, you will just use different numbers in the formula depending on what data is given to you.  

d:  With large sample sizes, the data often resembles normally distributed data, so we can still construct confidence intervals from the data.

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step-by-step explanation: