Download A Performance Assessment

A Performance Assessment
A bottling machine is operating with a standard deviation of 0.12 ounce. Suppose that in
an SRS of 36 bottles, the machine inserted an average of 16.1 ounces into each bottle.
Determine a 95% confidence interval for the mean number of ounces in all the bottles
this machine fills in one day.
Solution:
(1) Parameter:
 we are looking for an estimate of  .
 given σ = 0.12

_
given x = 16.1
(2) Conditions:





I – Independent: The population of bottles is sufficiently greater than 10x the
sample size. N > 10n
R- Random: we are told that the sample is random
O –Outliers: no reason to suggest that there are any outliers
N – Normal: nothing to indicate skewness
S - sample size is sufficiently large n > 30.
(3) Calculations:
Identify by name or by formula:
_
Confidence interval on x where σ is known.
OR: x  z *

n
 0.12 
 = 16.1 + 0.0392
 36 
= 16.1 + 1.96 
(4) I am 95% confident that the true mean number of ounces in a bottle for a particular
day is between 16.061 and 16.139 oz