Prehistoric cave paintings were discovered in a cave in france. the paint contained 26 % of the original carbon-14. use the exponential decay model for carbon-14, upper a equals upper a 0 e superscript negative 0.000121 t, to estimate the age of the paintings.

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.