00:01
Hello students, in the equation a, we asked to construct 95 % confidence interval and formula for that is given by x bar plus or minus z into sigma by square root of n.
00:18
So this gives us 1 .99 plus or minus 1 .96 into 0 .05 divided by square root of 100 and this gives us 95 % confidence interval is equal to 1 .9802 comma 1 .9998.
00:48
And the next question b, so the answer is yes.
00:57
To use the formula for calculating the confidence interval, we must assume that the population of soft drink that the population of soft drink fill is normally distributed.
01:41
This assumption is necessary because formula relies on properties of normal distribution.
01:46
Additionally, with a large sample size, the central limit theorem suggests that sampling distribution of the sample mean would be approximately normally distributed even the population is not normal.
01:56
Then the question c, the calculated confidence interval in the part a is 1 .9802 liters comma 1 .9998 liters.
02:12
This means we are 95 % confident that true population mean falls within this interval.
02:37
However, individual's bottle's fill level may vary and it is possible to find the bottle with amounts outside this confidence interval...