A manufacturer of pharmaceutical products analyzes each batch of a product to verify the concentration of the active ingredient. The chemical analysis is not perfectly precise. In fact, repeated measurements follow a normal distribution with mean

equal to the true concentration and standard deviation=0.0067

=0.0067grams per liter. Three analyses of one batch give concentrations of0.8959

0.8959,0.8712

0.8712, and0.8728

0.8728grams per liter. To estimate the true concentration, give a95%

95%confidence interval for

.

STATE: What is the concentration of the active ingredient in this batch?

PLAN: We will estimate the true concentration by giving a95%

95%confidence interval for the mean

of the distribution.

SOLVE: Find the mean of the measurements. (Enter your answer rounded to four decimal places.)

mean:

g/l

Determine the bounds of the95%

95%confidence interval for

. (Enter your answer rounded to four decimal places.)

lower bound:

upper bound:

CONCLUDE: We are95%

95%confident that the mean concentration of the active ingredient is between the values for the lower bound and the upper bound