(Solved): Use the standard normal distribution or the t-distribution to construct a \( 99 \% \) confidence i ...

Use the standard normal distribution or the t-distribution to construct a \( 99 \% \) confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a random sample of 42 people, the mean body mass index (BMI) was \( 29.1 \) and the standard deviation was \( 6.14 \). A. Use a normal distribution because the sample is random, \( n \geq 30 \), and \( \sigma \) is known. B. Use a t-distribution because the sample is random, the population is normal, and \( \sigma \) is unknown. C. Use a t-distribution because the sample is random, \( n \geq 30 \), and \( \sigma \) is unknown. D. Use a normal distribution because the sample is random, the population is normal, and \( \sigma \) is known. E. Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or \( n<30 \), and the population is not known to be normal. Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice. A. The \( 99 \% \) confidence interval is (Round to two decimal places as needed.) B. Neither distribution can be used to construct the confidence interval. Interpret the results. Choose the correct answer below. A. If a large sample of people are taken approximately \( 99 \% \) of them will have a BMI between the bounds of the confidence interval. B. With \( 99 \% \) confidence, it can be said that the population mean BMI is between the bounds of the confidence interval. C. It can be said that \( 99 \% \) of people have a BMI between the bounds of the confidence interval. D. Neither distribution can be used to construct the confidence interval.