Question

A manufacturer wants to purchase a certain product of foil. The foil is stored on 1534 rolls each containing a varying amount of foil with a standard deviation of 12.5. In order to estimate the total number of foil on all the rolls, the manufacturer randomly selected 200 rolls and measured the number of foil on each roll. The sample mean was 48. Then the 95% confidence interval to estimate the population mean of foil is between ____________.

Answer 1

Sample size = n = 200

Sample mean = = 48

T

Standard deviation = $\sigma$ = 12.5

Significance level = $\alpha$ = 1-0.95 = 0.05

At 0.05 significance level, the critical value of Z is

ZK12=20.05/2 =1.96 950). CI: CI+2&12X s = 48+1.96X12.5 V200 =48+1.7324 =(46.2676, 49.7324)

Therefore the 95% confidence interval to estimate the population mean of foil is between 46.27 and 49.73....(rounded to 2 decimal places)