Questions: Use the standard normal distribution or the t-distribution to construct a 90% 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 45 people, the mean body mass index (BMI) was 26.9 and the standard deviation was 6.12. Which distribution should be used to construct the confidence interval? Choose the correct answer below. A. Use a t-distribution because the sample is random, the population is normal, and σ is unknown. B. Use a t-distribution because the sample is random, n ≥ 30, and σ is unknown. C. Use a normal distribution because the sample is random, the population is normal, and σ is known. D. Use a normal distribution because the sample is random, n ≥ 30, and σ 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.

Transcript text: Use the standard normal distribution or the t-distribution to construct a $90 \%$ 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 45 people, the mean body mass index (BMI) was 26.9 and the standard deviation was 6.12. Which distribution should be used to construct the confidence interval? Choose the correct answer below. A. Use a $t$-distribution because the sample is random, the population is normal, and $\sigma$ is unknown. B. Use a t-distribution because the sample is random, $n \geq 30$, and $\sigma$ is unknown. C. Use a normal distribution because the sample is random, the population is normal, and $\sigma$ is known. D. Use a normal distribution because the sample is random, $n \geq 30$, and $\sigma$ is known. E. Neither a normal distribution nor a t-distribution can be used because either the sample is not random, or $\mathrm{n}<30$, and the population is not known to be normal.