A movie theater has had a poor accounting system. The manager has no idea how many large containers of popcorn are sold per movie showing. She knows that the amounts vary by day of the week and hour of the day. However, she wants to estimate the overall average per movie showing. To do so, she randomly selects 12 movie performances and counts the number of large containers of popcorn sold between 30 minutes before the movie showing and 15 minutes after the movie showing. The sample average was 43.7 containers, with a sample variance of 228. Construct a 95% confidence interval to estimate the mean number of large containers of popcorn sold during a movie showing. Assume the number of large containers of popcorn sold per movie is normally distributed in the population. Use this information to construct a 98% confidence interval to estimate the population variance.

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