The method of tree-ring dating gave the following years A.D. for an archaeological excavation site. Assume that the population ofxvalues has an approximately normal distribution.

1,306

1,180

1,264

1,292

1,257

1,257

1,271

1,215

(a)Find the sample mean yearxand sample standard deviations. (Round your answers to four decimal places.)

x= A.D.

s= yr

(b)When finding an90% confidence interval, what is the critical value for confidence level? (Give your answer to three decimal places.)

t_c=

What is the maximal margin of error when finding a90% confidence interval for the mean of all tree-ring dates from this archaeological site? (Round your answer to the nearest whole number.)

E=

Find a90% confidence interval for the mean of all tree-ring dates from this archaeological site. (Round your answers to the nearest whole number.)

lower limit A.D.

upper limit A.D.