Answer to Question #186657 in Statistics and Probability for Gwyneth Balete

Question

A coffee machine is regulated so that the amount of drink dispensed is approximately normally distributed with a standard deviation of 15 mm. Find the 95% confidence interval for the mean of all coffee drinks dispensed by this machine if the random sample of 36 drinks had an average content of 225 ml.

Answer 1

Critical value at 0.05 significance level z = ±1.96

The 95% confidence interval for the mean is

$225 - (1.96)\frac{15}{\sqrt{36}} < μ < 225 + (1.96) \frac{15}{\sqrt{36}} \\ 225 - 4.9 < μ < 225 + 4.9 \\ 220.1 < μ < 229.9$