Answer:
The confidence interval for the true mean calorie content is
[tex]215<\mu<245[/tex]
Step-by-step explanation:
In this problem we know the mean and standard deviation fo the sample, so we can compute the CI like this:
[tex]\bar{x}-t*s/\sqrt{n}< \mu<\bar{x}+t*s/\sqrt{n}[/tex]
We need to determine t for 10-1=9 degrees of freedom and 99% confidence level. We look up in the t-table and the value for t is 3.2498.
Then we can calculate the limits of the CI:
[tex]\bar{x}-t*s/\sqrt{n}< \mu<\bar{x}+t*s/\sqrt{n}\\\\230-3.2498*15/\sqrt{10}<\mu< 230+3.2498*15/\sqrt{10}\\\\230- 15.41515 <\mu< 230+15.41515\\\\215<\mu<245[/tex]
