Answer question **Transcription for Educational Website:**---**Question:**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 49 people, the mean body mass index (BMI) was 29.9 and the standard deviation was 6.03.**Options:**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, n ≥ 30, and σ is unknown.- **B.** Use a t-distribution because the sample is random, the population is normal, 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.**Instructions:**- Help Me Solve This- View an Example- Get More Help**Action:**Check Answer---**Explanation of Concepts:**- **Standard Normal Distribution vs. T-Distribution:** - The standard normal distribution is typically used when the population standard deviation is known and the sample size is large. - The t-distribution is used when the population standard deviation is not known, particularly with smaller sample sizes. However, it can also be used with larger samples when σ is unknown, as it becomes similar to the standard normal distribution.- **Confidence Interval Construction:** - A confidence interval provides a range of values that is likely to contain the population mean. The level (e.g., 99%) represents the degree of confidence in this range.- **Parameters:** - **n:** The sample size (n = 49). - **Mean (x̄):** The average BMI in the sample (29.9). - **Standard Deviation (s):** The sample standard deviation is 6.03. - **σ:** The population standard deviation (unknown here).Note: Always verify conditions before applying statistical methods to ensure accurate results.

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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 49 people, the mean body mass index (BMI) was 29.9 and the standard deviation was 6.03. Which distribution should be used to construct the confidence interval? Choose the correct answer below. O A. Use a t-distribution because the sample is random, n2 30, and o is unknown. O B. Use a t-distribution because the sample is random, the population is normal, and o is unknown. O C. Use a normal distribution because the sample is random, the population is normal, and o is known. O D. Use a normal distribution because the sample is random, n2 30, and o is known. OE. 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,